Quantum Field Theory & Gravity
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Quantum Field Theory & Gravity Quantum Field Theory & Gravity Understanding discoveries at the Energy, Intensity, and Cosmic Frontiers Get Expertise Rajan Gupta (505) 667-7664...
Quantum Field Theory and Representation Theory
Woit, Peter
Quantum Field Theory and Representation Theory Peter Woit woit@math.columbia.edu Department of Mathematics Columbia University Quantum Field Theory and Representation Theory p.1 #12;Outline of the talk · Quantum Mechanics and Representation Theory: Some History Quantum Field Theory and Representation Theory
Noncommutative Quantum Field Theories
H. O. Girotti
2003-03-19T23:59:59.000Z
We start by reviewing the formulation of noncommutative quantum mechanics as a constrained system. Then, we address to the problem of field theories defined on a noncommutative space-time manifold. The Moyal product is introduced and the appearance of the UV/IR mechanism is exemplified. The emphasis is on finding and analyzing noncommutative quantum field theories which are renormalizable and free of nonintegrable infrared singularities. In this last connection we give a detailed discussion of the quantization of the noncommutative Wess-Zumino model as well as of its low energy behavior.
Experimental quantum field theory
Bell, J S
1977-01-01T23:59:59.000Z
Presented here, is, in the opinion of the author, the essential minimum of quantum field theory that should be known to cultivated experimental particle physicists. The word experimental describes not only the audience aimed at but also the level of mathematical rigour aspired to. (0 refs).
Algebraic Quantum Field Theory
Hans Halvorson; Michael Mueger
2006-02-14T23:59:59.000Z
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of the theory, we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by S. Doplicher, R. Haag, and J. E. Roberts (DHR); and we give an alternative proof of Doplicher and Roberts' reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix.
Constructive Quantum Field Theory
Giovanni Gallavotti
2005-10-04T23:59:59.000Z
A review of the renormalization group approach to the proof of non perturbative ultraviolet stability in scalar field theories in dimension d=2,3.
Gerbes and quantum field theory
Jouko Mickelsson
2006-03-11T23:59:59.000Z
The basic mechanism how gerbes arise in quantum field theory is explained; in particular the case of chiral fermions in background fields is treated. The role of of various gauge group extensions (central extensions of loop groups and their generalizations) is also explained, in relation to index theory computation of the Dixmier-Douady class of a gerbe.
Quantum Field Theory in Graphene
I. V. Fialkovsky; D. V. Vassilevich
2011-11-18T23:59:59.000Z
This is a short non-technical introduction to applications of the Quantum Field Theory methods to graphene. We derive the Dirac model from the tight binding model and describe calculations of the polarization operator (conductivity). Later on, we use this quantity to describe the Quantum Hall Effect, light absorption by graphene, the Faraday effect, and the Casimir interaction.
Renormalization and quantum field theory
R. E. Borcherds
2011-03-09T23:59:59.000Z
The aim of this paper is to describe how to use regularization and renormalization to construct a perturbative quantum field theory from a Lagrangian. We first define renormalizations and Feynman measures, and show that although there need not exist a canonical Feynman measure, there is a canonical orbit of Feynman measures under renormalization. We then construct a perturbative quantum field theory from a Lagrangian and a Feynman measure, and show that it satisfies perturbative analogues of the Wightman axioms, extended to allow time-ordered composite operators over curved spacetimes.
A Naturally Renormalized Quantum Field Theory
S. Rouhani; M. V. Takook
2006-07-07T23:59:59.000Z
It was shown that quantum metric fluctuations smear out the singularities of Green's functions on the light cone [1], but it does not remove other ultraviolet divergences of quantum field theory. We have proved that the quantum field theory in Krein space, {\\it i.e.} indefinite metric quantization, removes all divergences of quantum field theory with exception of the light cone singularity [2,3]. In this paper, it is discussed that the combination of quantum field theory in Krein space together with consideration of quantum metric fluctuations, results in quantum field theory without any divergences.
Monte Carlo Methods in Quantum Field Theory
I. Montvay
2007-05-30T23:59:59.000Z
In these lecture notes some applications of Monte Carlo integration methods in Quantum Field Theory - in particular in Quantum Chromodynamics - are introduced and discussed.
RELATIVISTIC QUANTUM FIELD THEORY OF A HYPERNUCLEI
Boguta, J.
2013-01-01T23:59:59.000Z
0 Nuclei in Relativistic Field Theory of Nuclear Matter, LBLRelativistic Quantum Field Theory of Finite Nuclei, LBL prein a Relativistic Mean-Field Theory, Stanford preprint F.E.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V. [Moscow State University, Faculty of Physics (Russian Federation)] [Moscow State University, Faculty of Physics (Russian Federation); Mnatsakanova, M. N., E-mail: mnatsak@theory.sinp.msu.ru [Moscow State University, Skobeltsyn Institute of Nuclear Physics (Russian Federation); Vernov, Yu. S. [Russian Academy of Sciences, Institute for Nuclear Research (Russian Federation)] [Russian Academy of Sciences, Institute for Nuclear Research (Russian Federation)
2013-08-15T23:59:59.000Z
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Haag's Theorem in Noncommutative Quantum Field Theory
K. V. Antipin; M. N. Mnatsakanova; Yu. S. Vernov
2012-02-05T23:59:59.000Z
Haag's theorem was extended to noncommutative quantum field theory in a general case when time does not commute with spatial variables. It was proven that if S-matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in another theory is equal to unity as well. In fact this result is valid in any SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory.
Beyond the scalar Higgs, in lattice quantum field theory
Schroeder, Christopher Robert
2009-01-01T23:59:59.000Z
as an effective field theory . . . . . Higgs mass upperHiggs, in Lattice Quantum Field Theory by Christopher Robertin Lattice Quantum Field Theory A dissertation submitted in
Classical Theorems in Noncommutative Quantum Field Theory
M. Chaichian; M. Mnatsakanova; A. Tureanu; Yu. Vernov
2006-12-12T23:59:59.000Z
Classical results of the axiomatic quantum field theory - Reeh and Schlieder's theorems, irreducibility of the set of field operators and generalized Haag's theorem are proven in SO(1,1) invariant quantum field theory, of which an important example is noncommutative quantum field theory. In SO(1,3) invariant theory new consequences of generalized Haag's theorem are obtained. It has been proven that the equality of four-point Wightman functions in two theories leads to the equality of elastic scattering amplitudes and thus the total cross-sections in these theories.
Some Studies in Noncommutative Quantum Field Theories
Sunandan Gangopadhyay
2008-06-12T23:59:59.000Z
The central theme of this thesis is to study some aspects of noncommutative quantum mechanics and noncommutative quantum field theory. We explore how noncommutative structures can emerge and study the consequences of such structures in various physical models.
The quantum field theory interpretation of quantum mechanics
Alberto C. de la Torre
2015-03-02T23:59:59.000Z
It is shown that adopting the \\emph{Quantum Field} ---extended entity in space-time build by dynamic appearance propagation and annihilation of virtual particles--- as the primary ontology the astonishing features of quantum mechanics can be rendered intuitive. This interpretation of quantum mechanics follows from the formalism of the most successful theory in physics: quantum field theory.
Spinless Quantum Field Theory and Interpretation
Dong-Sheng Wang
2013-03-07T23:59:59.000Z
Quantum field theory is mostly known as the most advanced and well-developed theory in physics, which combines quantum mechanics and special relativity consistently. In this work, we study the spinless quantum field theory, namely the Klein-Gordon equation, and we find that there exists a Dirac form of this equation which predicts the existence of spinless fermion. For its understanding, we start from the interpretation of quantum field based on the concept of quantum scope, we also extract new meanings of wave-particle duality and quantum statistics. The existence of spinless fermion is consistent with spin-statistics theorem and also supersymmetry, and it leads to several new kinds of interactions among elementary particles. Our work contributes to the study of spinless quantum field theory and could have implications for the case of higher spin.
Axiomatic quantum field theory in curved spacetime
S. Hollands; R. M. Wald
2008-03-13T23:59:59.000Z
The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features--such as Poincare invariance and the existence of a preferred vacuum state--that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is locally and covariantly constructed from the spacetime metric), a microlocal spectrum condition, an "associativity" condition, and the requirement that the coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved spacetime versions of the spin-statistics theorem and the PCT theorem. Some potentially significant further implications of our new viewpoint on quantum field theory are discussed.
Functional Integration for Quantum Field Theory
J. LaChapelle
2006-10-16T23:59:59.000Z
The functional integration scheme for path integrals advanced by Cartier and DeWitt-Morette is extended to the case of fields. The extended scheme is then applied to quantum field theory. Several aspects of the construction are discussed.
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
Maroun, Michael Anthony
2013-01-01T23:59:59.000Z
The Unique Status of Condensed Matter Theory . . . . . . . .of a Satisfactory Theory . . . . . . . . . . . . BasicThe Generalized Quantum Theory The Postulates and Philosophy
Computer Stochastics in Scalar Quantum Field Theory
C. B. Lang
1993-12-01T23:59:59.000Z
This is a series of lectures on Monte Carlo results on the non-perturbative, lattice formulation approach to quantum field theory. Emphasis is put on 4D scalar quantum field theory. I discuss real space renormalization group, fixed point properties and logarithmic corrections, partition function zeroes, the triviality bound on the Higgs mass, finite size effects, Goldstone bosons and chiral perturbation theory, and the determination of scattering phase shifts for some scalar models.
Quantum field theory and the Standard Model
W. Hollik
2010-12-17T23:59:59.000Z
In this lecture we discuss the basic ingredients for gauge invariant quantum field theories. We give an introduction to the elements of quantum field theory, to the construction of the basic Lagrangian for a general gauge theory, and proceed with the formulation of QCD and the electroweak Standard Model with electroweak symmetry breaking via the Higgs mechanism. The phenomenology of W and Z bosons is discussed and implications for the Higgs boson are derived from comparison with experimental precision data.
Quantum Field Theory Mark Srednicki
Akhmedov, Azer
The Spin-Statistics Theorem (3) 45 5 The LSZ Reduction Formula (3) 49 6 Path Integrals in Quantum Mechanics Quantization of Spinor Fields II (38) 246 40 Parity, Time Reversal, and Charge Conjugation (23, 39) 254 #12, 59) 369 #12;6 63 The Vertex Function in Spinor Electrodynamics (62) 378 64 The Magnetic Moment
Lessons in quantum gravity from quantum field theory
Berenstein, David [Department of Physics, University of California at Santa Barbara, CA 93106 (United States); Institute for Advanced Study, School of Natural Science, Princeton, NJ 08540 (United States)
2010-12-07T23:59:59.000Z
This paper reviews advances in the understanding of quantum gravity based on field theory calculations in the AdS/CFT correspondence.
Some convolution products in Quantum Field Theory
Herintsitohaina Ratsimbarison
2006-12-05T23:59:59.000Z
This paper aims to show constructions of scale dependence and interaction on some probabilistic models which may be revelant for renormalization theory in Quantum Field Theory. We begin with a review of the convolution product's use in the Kreimer-Connes formalism of perturbative renormalization. We show that the Wilson effective action can be obtained from a convolution product propriety of regularized Gaussian measures on the space of fields. Then, we propose a natural C*-algebraic framework for scale dependent field theories which may enhance the conceptual approach to renormalization theory. In the same spirit, we introduce a probabilistic construction of interacting theories for simple models and apply it for quantum field theory by defining a partition function in this setting.
Noncommutative Deformations of Wightman Quantum Field Theories
Harald Grosse; Gandalf Lechner
2008-08-26T23:59:59.000Z
Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman theory, we consider special vacuum representations of its Weyl-Wigner deformed counterpart. In such representations, the effect of the noncommutativity on the basic structures of Wightman theory, in particular the covariance, locality and regularity properties of the fields, the structure of the Wightman functions, and the commutative limit, is analyzed. Despite the nonlocal structure introduced by the noncommutativity, the deformed quantum fields can still be localized in certain wedge-shaped regions, and may therefore be used to compute noncommutative corrections to two-particle S-matrix elements.
Algebraic conformal quantum field theory in perspective
Karl-Henning Rehren
2015-01-14T23:59:59.000Z
Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete classifications. The structural insights, analytical methods and constructive tools are expected to be useful also for four-dimensional QFT.
General Covariance in Algebraic Quantum Field Theory
Romeo Brunetti; Martin Porrmann; Giuseppe Ruzzi
2005-12-17T23:59:59.000Z
In this review we report on how the problem of general covariance is treated within the algebraic approach to quantum field theory by use of concepts from category theory. Some new results on net cohomology and superselection structure attained in this framework are included.
Wavelet-Based Quantum Field Theory
Mikhail V. Altaisky
2007-11-11T23:59:59.000Z
The Euclidean quantum field theory for the fields $\\phi_{\\Delta x}(x)$, which depend on both the position $x$ and the resolution $\\Delta x$, constructed in SIGMA 2 (2006), 046, hep-th/0604170, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.
221B Lecture Notes Quantum Field Theory III (Radiation Field)
Murayama, Hitoshi
221B Lecture Notes Quantum Field Theory III (Radiation Field) 1 Quantization of Radiation Field was quantized: photons. Now that we have gone through quantization of a classical field (Schr¨odinger field so far), we can proceed to quantize the Maxwell field. The basic idea is pretty much the same, except
221B Lecture Notes Quantum Field Theory IV (Radiation Field)
Murayama, Hitoshi
221B Lecture Notes Quantum Field Theory IV (Radiation Field) 1 Quantization of Radiation Field was quantized: photons. Now that we have gone through quantization of a classical field (Schr¨odinger field so far), we can proceed to quantize the Maxwell field. The basic idea is pretty much the same, except
Quantum Field Theory on Noncommutative Spaces
Richard J. Szabo
2003-01-23T23:59:59.000Z
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative Yang-Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study of the gauge group of noncommutative Yang-Mills theory. Some of the more mathematical ideas and techniques of noncommutative geometry are also briefly explained.
3D Quantum Gravity and Effective Noncommutative Quantum Field Theory
Freidel, Laurent; Livine, Etera R. [Perimeter Institute, 31 Caroline Street, North Waterloo, Ontario N2L 2Y5, Canada, and Laboratoire de Physique, ENS Lyon, CNRS UMR 5672, 46 Allee d'Italie, 69364 Lyon Cedex 07 (France)
2006-06-09T23:59:59.000Z
We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a {kappa} deformation of the Poincare group.
Quantum field theory of relic nonequilibrium systems
Nicolas G. Underwood; Antony Valentini
2014-11-14T23:59:59.000Z
In terms of the de Broglie-Bohm pilot-wave formulation of quantum theory, we develop field-theoretical models of quantum nonequilibrium systems which could exist today as relics from the very early universe. We consider relic excited states generated by inflaton decay, as well as relic vacuum modes, for particle species that decoupled close to the Planck temperature. Simple estimates suggest that, at least in principle, quantum nonequilibrium could survive to the present day for some relic systems. The main focus of this paper is to describe the behaviour of such systems in terms of field theory, with the aim of understanding how relic quantum nonequilibrium might manifest experimentally. We show by explicit calculation that simple perturbative couplings will transfer quantum nonequilibrium from one field to another (for example from the inflaton field to its decay products). We also show that fields in a state of quantum nonequilibrium will generate anomalous spectra for standard energy measurements. Possible connections to current astrophysical observations are briefly addressed.
Mathematical definition of quantum field theory on a manifold
A. V. Stoyanovsky
2009-11-21T23:59:59.000Z
We give a mathematical definition of quantum field theory on a manifold, and definition of quantization of a classical field theory given by a variational principle.
Noncommutative Time in Quantum Field Theory
Tapio Salminen; Anca Tureanu
2011-07-19T23:59:59.000Z
We analyze, starting from first principles, the quantization of field theories, in order to find out to which problems a noncommutative time would possibly lead. We examine the problem in the interaction picture (Tomonaga-Schwinger equation), the Heisenberg picture (Yang-Feldman-K\\"all\\'{e}n equation) and the path integral approach. They all indicate inconsistency when time is taken as a noncommutative coordinate. The causality issue appears as the key aspect, while the unitarity problem is subsidiary. These results are consistent with string theory, which does not admit a time-space noncommutative quantum field theory as its low-energy limit, with the exception of light-like noncommutativity.
Undergraduate Lecture Notes in Topological Quantum Field Theory
Vladimir G. Ivancevic; Tijana T. Ivancevic
2008-12-11T23:59:59.000Z
These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism. Keywords: quantum mechanics/field theory, path integral, Hodge decomposition, Chern-Simons and Yang-Mills gauge theories, conformal field theory
Remarks on twisted noncommutative quantum field theory
Zahn, Jochen [II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)
2006-05-15T23:59:59.000Z
We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the twisted structure is so rigid that it is hard to derive any predictions, unless one gives up general principles of quantum theory. It is also shown that the twisted structure is not responsible for the presence or absence of UV/IR-mixing, as claimed in the literature.
Quantum Field Theory & Gravity
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Physics 221B: Solution to HW # 8 Quantum Field Theory
Murayama, Hitoshi
Physics 221B: Solution to HW # 8 Quantum Field Theory 1) Bosonic Grand-Partition Function The solution to this problem is outlined clearly in the beginning of the lecture notes `Quantum Field Theory II
Functorial Quantum Field Theory in the Riemannian setting
Santosh Kandel
2015-02-25T23:59:59.000Z
We construct examples of Functorial Quantum Field Theories in the Riemannian setting by quantizing free massive bosons.
Noncommutative Quantum Mechanics from Noncommutative Quantum Field Theory
Pei-Ming Ho; Hsien-Chung Kao
2001-10-26T23:59:59.000Z
We derive noncommutative multi-particle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Paricles of opposite charges are found to have opposite noncommutativity. As a result, there is no noncommutative correction to the hydrogen atom spectrum at the tree level. We also comment on the obstacles to take noncommutative phenomenology seriously, and propose a way to construct noncommutative SU(5) grand unified theory.
Aspects of locally covariant quantum field theory
Ko Sanders
2008-09-28T23:59:59.000Z
This thesis considers various aspects of locally covariant quantum field theory (LCQFT; see Brunetti et al., Commun.Math.Phys. 237 (2003), 31-68), a mathematical framework to describe axiomatic quantum field theories in curved spacetimes. New results include: a philosophical interpretation of certain aspects of this framework in terms of modal logic; a proof that the truncated n-point functions of any Hadamard state of the free real scalar field are smooth, except for n=2; a description of he free Dirac field in a representation independent way, showing that the theory is determined entirely by the relations between the adjoint map, the charge conjugation map and the Dirac operator; a proof that the relative Cauchy evolution of the free Dirac field is related to its stress-energy-momentum tensor in the same way as for the free real scalar field (cf. loc.cit.); several results on the Reeh-Schlieder property in LCQFT, including but not limited to those of our earlier paper; a new and elegant approach to wave front sets of Banach space-valued distributions, which allows easy proofs and extensions of results in the literature.
Quantum Jet Theory I: Free fields
T. A. Larsson
2007-01-18T23:59:59.000Z
QJT (Quantum Jet Theory) is the quantum theory of jets, which can be canonically identified with truncated Taylor series. Ultralocality requires a novel quantization scheme, where dynamics is treated as a constraint in the history phase space. QJT differs from QFT since it involves a new datum: the expansion point. This difference is substantial because it leads to new gauge and diff anomalies, which are necessary to combine background independence with locality. Physically, the new ingredient is that the observer's trajectory is explicitly introduced and quantized together with the fields. In this paper the harmonic oscillator and free fields are treated within QJT, correcting previous flaws. The standard Hilbert space is recovered for the harmonic oscillator, but there are interesting modifications already for the free scalar field, due to quantization of the observer's trajectory. Only free fields are treated in detail, but the complications when interactions are introduced are briefly discussed. We also explain why QJT is necessary to resolve the conceptual problems of quantum gravity.
Mossbauer neutrinos in quantum mechanics and quantum field theory
Kopp, Joachim
2009-01-01T23:59:59.000Z
We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detecti...
Nonlinear quantum equations: Classical field theory
Rego-Monteiro, M. A.; Nobre, F. D. [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)] [Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro - RJ (Brazil)
2013-10-15T23:59:59.000Z
An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q? 1. The main characteristic of this field theory consists on the fact that besides the usual ?(x(vector sign),t), a new field ?(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field ?(x(vector sign),t), which is defined by means of an additional equation, becomes ?{sup *}(x(vector sign),t) only when q? 1. The solutions for the fields ?(x(vector sign),t) and ?(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.
Quantum simulation of quantum field theory using continuous variables
Kevin Marshall; Raphael Pooser; George Siopsis; Christian Weedbrook
2015-03-27T23:59:59.000Z
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has led to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is believed to be hard using a classical computer. Building on this, we give an experimental implementation based on cluster states that is feasible with today's technology.
Rigorous Definition of Quantum Field Operators in Noncommutative Quantum Field Theory
M. N. Mnatsakanova; Yu. S. Vernov
2010-02-07T23:59:59.000Z
The space, on which quantum field operators are given, is constructed in any theory, in which the usual product between test functions is substituted by the $\\star$-product (the Moyal-type product). The important example of such a theory is noncommutative quantum field theory (NC QFT). This construction is the key point in the derivation of the Wightman reconstruction theorem.
Algebraic quantum field theory in curved spacetimes
Christopher J. Fewster; Rainer Verch
2015-04-02T23:59:59.000Z
This article sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor from a category of spacetimes to a category of ($C^*$)-algebras obeying supplementary conditions. Among other things: (a) the key idea of relative Cauchy evolution is described in detail, and related to the stress-energy tensor; (b) a systematic "rigidity argument" is used to generalise results from flat to curved spacetimes; (c) a detailed discussion of the issue of selection of physical states is given, linking notions of stability at microscopic, mesoscopic and macroscopic scales; (d) the notion of subtheories and global gauge transformations are formalised; (e) it is shown that the general framework excludes the possibility of there being a single preferred state in each spacetime, if the choice of states is local and covariant. Many of the ideas are illustrated by the example of the free Klein-Gordon theory, which is given a new "universal definition".
Deformation Quantization: From Quantum Mechanics to Quantum Field Theory
P. Tillman
2006-10-31T23:59:59.000Z
The aim of this paper is to give a basic overview of Deformation Quantization (DQ) to physicists. A summary is given here of some of the key developments over the past thirty years in the context of physics, from quantum mechanics to quantum field theory. Also, we discuss some of the conceptual advantages of DQ and how DQ may be related to algebraic quantum field theory. Additionally, our previous results are summarized which includes the construction of the Fedosov star-product on dS/AdS. One of the goals of these results was to verify that DQ gave the same results as previous analyses of these spaces. Another was to verify that the formal series used in the conventional treatment converged by obtaining exact and nonperturbative results for these spaces.
Causality and chance in relativistic quantum field theories
Richard Healey
2014-05-13T23:59:59.000Z
Bell appealed to the theory of relativity in formulating his principle of local causality. But he maintained that quantum field theories do not conform to that principle, even when their field equations are relativistically covariant and their observable algebras satisfy a relativistically motivated microcausality condition. A pragmatist view of quantum theory and an interventionist approach to causation prompt the reevaluation of local causality and microcausality. Local causality cannot be understood as a reasonable requirement on relativistic quantum field theories: it is unmotivated even if applicable to them. But microcausality emerges as a sufficient condition for the consistent application of a relativistic quantum field theory.
Radiation reaction in quantum field theory
Atsushi Higuchi
2004-03-30T23:59:59.000Z
We investigate radiation-reaction effects for a charged scalar particle accelerated by an external potential realized as a space-dependent mass term in quantum electrodynamics. In particular, we calculate the position shift of the final-state wave packet of the charged particle due to radiation at lowest order in the fine structure constant alpha and in the small h-bar approximation. We show that it disagrees with the result obtained using the Lorentz-Dirac formula for the radiation-reaction force, and that it agrees with the classical theory if one assumes that the particle loses its energy to radiation at each moment of time according to the Larmor formula in the static frame of the potential. However, the discrepancy is much smaller than the Compton wavelength of the particle. We also point out that the electromagnetic correction to the potential has no classical limit. (Correction. Surface terms were erroneously discarded to arrive at Eq. (59). By correcting this error we find that the position shift according to the Lorentz-Dirac theory obtained from Eq. (12) is reproduced by quantum field theory in the hbar -> 0 limit. We also find that the small V(z) approximation is unnecessary for this agreement. See Sec. VII.)
The effective field theory treatment of quantum gravity
Donoghue, John F. [Department of Physics, University of Massachusetts, Amherst, MA 01003 (United States)
2012-09-24T23:59:59.000Z
This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime.
Irreducibility of the set of field operators in Noncommutative Quantum Field Theory
M. N. Mnatsakanova; Yu. S. Vernov
2012-09-02T23:59:59.000Z
Irreducibility of the set of quantum field operators has been proved in noncommutative quantum field theory in the general case when time does not commute with spatial variables.
Mossbauer neutrinos in quantum mechanics and quantum field theory
Joachim Kopp
2009-06-12T23:59:59.000Z
We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence, and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detection cross section, including localization and Lamb-Mossbauer terms, cannot be predicted in quantum mechanics and have to be put in by hand.
Some differences between Dirac's hole theory and quantum field theory
Dan Solomon
2005-06-30T23:59:59.000Z
Diracs hole theory (HT) and quantum field theory (QFT) are generally considered to be equivalent to each other. However, it has been recently shown by several researchers that this is not necessarily the case. When the change in the vacuum energy was calculated for a time independent perturbation HT and QFT yielded different results. In this paper we extend this discussion to include a time dependent perturbation for which the exact solution to the Dirac equation is known. It will be shown that for this case, also, HT and QFT yield different results. In addition, there will be some discussion of the problem of anomalies in QFT.
Energy Inequalities in Quantum Field Theory
Christopher J. Fewster
2005-01-31T23:59:59.000Z
Quantum fields are known to violate all the pointwise energy conditions of classical general relativity. We review the subject of quantum energy inequalities: lower bounds satisfied by weighted averages of the stress-energy tensor, which may be regarded as the vestiges of the classical energy conditions after quantisation. Contact is also made with thermodynamics and related issues in quantum mechanics, where such inequalities find analogues in sharp Gaarding inequalities.
Nonlocal Quantization Principle in Quantum Field Theory and Quantum Gravity
Martin Kober
2014-10-21T23:59:59.000Z
In this paper a nonlocal generalization of field quantization is suggested. This quantization principle presupposes the assumption that the commutator between a field operator an the operator of the canonical conjugated variable referring to other space-time points does not vanish as it is postulated in the usual setting of quantum field theory. Based on this presupposition the corresponding expressions for the field operators, the eigenstates and the path integral formula are determined. The nonlocal quantization principle also leads to a generalized propagator. If the dependence of the commutator between operators on different space-time points on the distance of these points is assumed to be described by a Gaussian function, one obtains that the propagator is damped by an exponential. This leads to a disappearance of UV divergences. The transfer of the nonlocal quantization principle to canonical quantum gravity is considered as well. In this case the commutator has to be assumed to depend also on the gravitational field, since the distance between two points depends on the metric field.
Quantum Solution to Scalar Field Theory Models
Gordon Chalmers
2005-09-08T23:59:59.000Z
Amplitudes $A_n$ in $d$-dimensional scalar field theory are generated, to all orders in the coupling constant and at $n$-point. The amplitudes are expressed as a series in the mass $m$ and coupling $\\lambda$. The inputs are the classical scattering, and these generate, after the integrals are performed, the series expansion in the couplings $\\lambda_i$. The group theory of the scalar field theory leads to an additional permutation on the $L$ loop trace structures. Any scalar field theory, including those with higher dimension operators and in any dimension, are amenable.
Quantum chiral field theory of $0^{-+}$ glueball
Bing An Li
2011-08-23T23:59:59.000Z
A chiral field theory of $0^{-+}$ glueball is presented. The coupling between the quark operator and the $0^{-+}$ glueball field is revealed from the U(1) anomaly. The Lagrangian of this theory is constructed by adding a $0^{-+}$ glueball field to a successful Lagrangian of chiral field theory of pseudoscalar, vector, and axial-vector mesons. Quantitative study of the physical processes of the $0^{-+}$ glueball of $m=1.405\\textrm{GeV}$ is presented. The theoretical predictions can be used to identify the $0^{-+}$ glueball.
Twists of quantum groups and noncommutative field theory
P. P. Kulish
2006-06-07T23:59:59.000Z
The role of quantum universal enveloping algebras of symmetries in constructing a noncommutative geometry of space-time and corresponding field theory is discussed. It is shown that in the framework of the twist theory of quantum groups, the noncommutative (super) space-time defined by coordinates with Heisenberg commutation relations, is (super) Poincar\\'e invariant, as well as the corresponding field theory. Noncommutative parameters of global transformations are introduced.
Renormalization of Noncommutative Quantum Field Theories
Amilcar R. de Queiroz; Rahul Srivastava; Sachindeo Vaidya
2013-02-14T23:59:59.000Z
We report on a comprehensive analysis of the renormalization of noncommutative \\phi^4 scalar field theories on the Groenewold-Moyal (GM) plane. These scalar field theories are twisted Poincar\\'e invariant. Our main results are that these scalar field theories are renormalizable, free of UV/IR mixing, possess the same fixed points and \\beta-functions for the couplings as their commutative counterparts. We also argue that similar results hold true for any generic noncommutative field theory with polynomial interactions and involving only pure matter fields. A secondary aim of this work is to provide a comprehensive review of different approaches for the computation of the noncommutative S-matrix: noncommutative interaction picture and noncommutative LSZ formalism.
On a Formulation of Qubits in Quantum Field Theory
Jacques Calmet; Xavier Calmet
2012-01-21T23:59:59.000Z
Qubits have been designed in the framework of quantum mechanics. Attempts to formulate the problem in the language of quantum field theory have been proposed already. In this short note we refine the meaning of qubits within the framework of quantum field theory. We show that the notion of gauge invariance naturally leads to a generalization of qubits to QFTbits which are then the fundamental carriers of information from the quantum field theoretical point of view. The goal of this note is to stress the availability of such a generalized concept of QFTbits.
A Process Algebra Approach to Quantum Field Theory
William Sulis
2015-02-09T23:59:59.000Z
The process algebra has been used successfully to provide a novel formulation of quantum mechanics in which non-relativistic quantum mechanics (NRQM) emerges as an effective theory asymptotically. The process algebra is applied here to the formulation of quantum field theory. The resulting QFT is intuitive, free from divergences and eliminates the distinction between particle, field and wave. There is a finite, discrete emergent space-time on which arise emergent entities which transfer information like discrete waves and interact with measurement processes like particles. The need for second quantization is eliminated and the particle and field theories rest on a common foundation, clarifying and simplifying the relationship between the two.
The Physical Renormalization of Quantum Field Theories
Binger, Michael William.; /Stanford U., Phys. Dept. /SLAC
2007-02-20T23:59:59.000Z
The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, {alpha}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}), depends on three momentum scales and gives rise to an effective scale Q{sub eff}{sup 2}(k{sub 1}{sup 2}, k{sub 2}{sup 2}, k{sub 3}{sup 2}) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi-scale analytic renormalization scheme based on gauge-invariant Green's functions, in which the scale ambiguity problem is reduced since physical kinematic invariants determine the arguments of the couplings.
Viscosity, Black Holes, and Quantum Field Theory
D. T. Son; A. O. Starinets
2007-07-11T23:59:59.000Z
We review recent progress in applying the AdS/CFT correspondence to finite-temperature field theory. In particular, we show how the hydrodynamic behavior of field theory is reflected in the low-momentum limit of correlation functions computed through a real-time AdS/CFT prescription, which we formulate. We also show how the hydrodynamic modes in field theory correspond to the low-lying quasinormal modes of the AdS black p-brane metric. We provide a proof of the universality of the viscosity/entropy ratio within a class of theories with gravity duals and formulate a viscosity bound conjecture. Possible implications for real systems are mentioned.
Ordinary versus PT-symmetric ?³ quantum field theory
DOE Public Access Gateway for Energy & Science Beta (PAGES Beta)
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
2012-04-01T23:59:59.000Z
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric ig?³ quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian g?³ quantum field theory with those of the PT-symmetric ig?³ quantum field theory. It is shown that while the conventional g?³ theory in d=6 dimensions is asymptotically free, the ig?³ theory is like a g?? theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.
Quantum Mind from a Classical Field Theory of the Brain
Paola Zizzi
2011-04-13T23:59:59.000Z
We suggest that, with regard to a theory of quantum mind, brain processes can be described by a classical, dissipative, non-abelian gauge theory. In fact, such a theory has a hidden quantum nature due to its non-abelian character, which is revealed through dissipation, when the theory reduces to a quantum vacuum, where temperatures are of the order of absolute zero, and coherence of quantum states is preserved. We consider in particular the case of pure SU(2) gauge theory with a special anzatz for the gauge field, which breaks Lorentz invariance. In the ansatz, a contraction mapping plays the role of dissipation. In the limit of maximal dissipation, which corresponds to the attractive fixed point of the contraction mapping, the gauge fields reduce, up to constant factors, to the Pauli quantum gates for one-qubit states. Then tubuline-qubits can be processed in the quantum vacuum of the classical field theory of the brain, where decoherence is avoided due to the extremely low temperature. Finally, we interpret the classical SU(2) dissipative gauge theory as the quantum metalanguage (relative to the quantum logic of qubits), which holds the non-algorithmic aspect of the mind.
Hadamard subtractions for infrared singularities in quantum field theory
Burton, George Edmund C.
2011-06-27T23:59:59.000Z
Feynman graphs in perturbative quantum field theory are replete with infrared divergences caused by the presence of massless particles, how-ever these divergences are known to cancel order-by-order when all virtual and ...
Rigorous results in space-space noncommutative quantum field theory
M. N. Mnatsakanova; Yu. S. Vernov
2006-12-19T23:59:59.000Z
The axiomatic approach based on Wightman functions is developed in noncommutative quantum field theory. We have proved that the main results of the axiomatic approach remain valid if the noncommutativity affects only the spatial variables.
A Goldstone Theorem in Thermal Relativistic Quantum Field Theory
Christian D. Jaekel; Walter F. Wreszinski
2010-06-01T23:59:59.000Z
We prove a Goldstone Theorem in thermal relativistic quantum field theory, which relates spontaneous symmetry breaking to the rate of space-like decay of the two-point function. The critical rate of fall-off coincides with that of the massless free scalar field theory. Related results and open problems are briefly discussed.
Lorentz symmetry breaking as a quantum field theory regulator
Visser, Matt [School of Mathematics, Statistics, and Operations Research, Victoria University of Wellington, Wellington 6140 (New Zealand)
2009-07-15T23:59:59.000Z
Perturbative expansions of quantum field theories typically lead to ultraviolet (short-distance) divergences requiring regularization and renormalization. Many different regularization techniques have been developed over the years, but most regularizations require severe mutilation of the logical foundations of the theory. In contrast, breaking Lorentz invariance, while it is certainly a radical step, at least does not damage the logical foundations of the theory. I shall explore the features of a Lorentz symmetry breaking regulator in a simple polynomial scalar field theory and discuss its implications. In particular, I shall quantify just 'how much' Lorentz symmetry breaking is required to fully regulate the quantum theory and render it finite. This scalar field theory provides a simple way of understanding many of the key features of Horava's recent article [Phys. Rev. D 79, 084008 (2009)] on 3+1 dimensional quantum gravity.
Noncommutative Field Theory from Quantum Mechanical Space-Space Noncommutativity
Marcos Rosenbaum; J. David Vergara; L. Roman Juarez
2007-09-21T23:59:59.000Z
We investigate the incorporation of space noncommutativity into field theory by extending to the spectral continuum the minisuperspace action of the quantum mechanical harmonic oscillator propagator with an enlarged Heisenberg algebra. In addition to the usual $\\star$-product deformation of the algebra of field functions, we show that the parameter of noncommutativity can occur in noncommutative field theory even in the case of free fields without self-interacting potentials.
The Monte Carlo method in quantum field theory
Colin Morningstar
2007-02-20T23:59:59.000Z
This series of six lectures is an introduction to using the Monte Carlo method to carry out nonperturbative studies in quantum field theories. Path integrals in quantum field theory are reviewed, and their evaluation by the Monte Carlo method with Markov-chain based importance sampling is presented. Properties of Markov chains are discussed in detail and several proofs are presented, culminating in the fundamental limit theorem for irreducible Markov chains. The example of a real scalar field theory is used to illustrate the Metropolis-Hastings method and to demonstrate the effectiveness of an action-preserving (microcanonical) local updating algorithm in reducing autocorrelations. The goal of these lectures is to provide the beginner with the basic skills needed to start carrying out Monte Carlo studies in quantum field theories, as well as to present the underlying theoretical foundations of the method.
Schwinger functions in noncommutative quantum field theory
Dorothea Bahns
2009-08-31T23:59:59.000Z
It is shown that the $n$-point functions of scalar massive free fields on the noncommutative Minkowski space are distributions which are boundary values of analytic functions. Contrary to what one might expect, this construction does not provide a connection to the popular traditional Euclidean approach to noncommutative field theory (unless the time variable is assumed to commute). Instead, one finds Schwinger functions with twistings involving only momenta that are on the mass-shell. This explains why renormalization in the traditional Euclidean noncommutative framework crudely differs from renormalization in the Minkowskian regime.
Young's Double Slit Experiment in Quantum Field Theory
Masakatsu Kenmoku; Kenji Kume
2011-03-01T23:59:59.000Z
Young's double slit experiment is formulated in the framework of canonical quantum field theory in view of the modern quantum optics. We adopt quantum scalar fields instead of quantum electromagnetic fields ignoring the vector freedom in gauge theory. The double slit state is introduced in Fock space corresponding to experimental setup. As observables, expectation values of energy density and positive frequency part of current with respect to the double slit state are calculated which give the interference term. Classical wave states are realized by coherent double slit states in Fock space which connect quantum particle states with classical wave states systematically. In case of incoherent sources, the interference term vanishes by averaging random phase angles as expected.
Radiation reaction in quantum field theory
Higuchi, A
2002-01-01T23:59:59.000Z
We investigate radiation-reaction effects for a charged scalar particle accelerated by an external potential realized as a space-dependent mass term in quantum electrodynamics. In particular, we calculate the position shift of the final-state wave packet of the charged particle due to radiation at lowest order in the fine structure constant alpha and in the small h-bar approximation. This quantity turns out to be much smaller than the width of the wave packet but can be compared with the classical counterpart. We show that it disagrees with the result obtained using the Abraham-Lorentz-Dirac formula for the radiation-reaction force, and that it agrees with the classical theory if one assumes that the particle loses its energy to radiation at each moment of time according to the Larmor formula in the static frame of the potential. We also point out that the electromagnetic correction to the potential has no classical limit.
Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field Theory
Giovanni Landi; Fedele Lizzi; Richard J. Szabo
2004-01-20T23:59:59.000Z
We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two circles. The matrix quantum mechanics is applied to the perturbative dynamics of scalar field theory, to tachyon dynamics in string field theory, and to the Hamiltonian dynamics of noncommutative gauge theory in two dimensions. We also describe the adiabatic dynamics of solitons on the noncommutative torus and compare various classes of noncommutative solitons on the torus and the plane.
Localization and diffusion in polymer quantum field theory
Michele Arzano; Marco Letizia
2014-08-13T23:59:59.000Z
Polymer quantization is a non-standard approach to quantizing a classical system inspired by background independent approaches to quantum gravity such as loop quantum gravity. When applied to field theory it introduces a characteristic polymer scale at the level of the fields classical configuration space. Compared with models with space-time discreteness or non-commutativity this is an alternative way in which a characteristic scale can be introduced in a field theoretic context. Motivated by this comparison we study here localization and diffusion properties associated with polymer field observables and dispersion relation in order to shed some light on the novel physical features introduced by polymer quantization. While localization processes seems to be only mildly affected by polymer effects, we find that polymer diffusion differs significantly from the "dimensional reduction" picture emerging in other Planck-scale models beyond local quantum field theory.
Generalized Gravity I : Kinematical Setting and reformalizing Quantum Field Theory
Johan Noldus
2008-04-20T23:59:59.000Z
The first part of this work deals with the development of a natural differential calculus on non-commutative manifolds. The second part extends the covariance and equivalence principle as well studies its kinematical consequences such as the arising of gauge theory. Furthermore, a manifestly causal and covariant formulation of quantum field theory is presented which surpasses the usual Hamiltonian and path integral construction. A particular representation of this theory on the kinematical structure developed in section three is moreover given.
Noncommutative and Non-Anticommutative Quantum Field Theory
J. W. Moffat
2001-07-19T23:59:59.000Z
A noncommutative and non-anticommutative quantum field theory is formulated in a superspace, in which the superspace coordinates satisfy noncommutative and non-anticommutative relations. A perturbative scalar field theory is investigated in which only the non-anticommutative algebraic structure is kept, and one loop diagrams are calculated and found to be finite due to the damping caused by a Gaussian factor in the propagator.
Theory of a quantum noncanonical field in curved spacetimes
Indurain, Javier; Liberati, Stefano [Departamento de Fisica Teorica, Universidad de Zaragoza, Zaragoza 50009 (Spain); SISSA, Via Beirut 2-4, 34151 Trieste (Italy) and INFN sezione di Trieste (Italy)
2009-08-15T23:59:59.000Z
Much attention has been recently devoted to the possibility that quantum gravity effects could lead to departures from special relativity in the form of a deformed Poincare algebra. These proposals go generically under the name of doubly or deformed special relativity (DSR). In this article we further explore a recently proposed class of quantum field theories, involving noncanonically commuting complex scalar fields, which have been shown to entail a DSR-like symmetry. An open issue for such theories is whether the DSR-like symmetry has to be taken as a physically relevant symmetry, or if in fact the 'true' symmetries of the theory are just rotations and translations while boost invariance has to be considered broken. Here we analyze this issue by extending the known results to curved spacetime under both of the previous assumptions. We show that if the symmetry of the free theory is taken to be a DSR-like realization of the Poincare symmetry, then it is not possible to render such a symmetry a gauge symmetry of the curved physical spacetime. However, it is possible to introduce an auxiliary spacetime which allows one to describe the theory as a standard quantum field theory in curved spacetime. Alternatively, taking the point of view that the noncanonical commutation of the fields actually implies a breakdown of boost invariance, the physical spacetime manifold has to be foliated in surfaces of simultaneity, and the field theory can be coupled to gravity by making use of the Arnowitt-Deser-Misner prescription.
The Boltzmann Equation in Classical and Quantum Field Theory
Sangyong Jeon
2005-07-18T23:59:59.000Z
Improving upon the previous treatment by Mueller and Son, we derive the Boltzmann equation that results from a classical scalar field theory. This is obtained by starting from the corresponding quantum field theory and taking the classical limit with particular emphasis on the path integral and perturbation theory. A previously overlooked Van-Vleck determinant is shown to control the tadpole type of self-energy that can still appear in the classical perturbation theory. Further comments on the validity of the approximations and possible applications are also given.
Noncommutative Common Cause Principles in Algebraic Quantum Field Theory
Gábor Hofer-Szabó; Péter Vecsernyés
2012-01-23T23:59:59.000Z
States in algebraic quantum field theory "typically" establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V_A and V_B, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V_A and V_B and the set {C, non-C} screens off the correlation between A and B.
Quantum statistical correlations in thermal field theories: Boundary effective theory
Bessa, A. [Escola de Ciencias e Tecnologia, Universidade Federal do Rio Grande do Norte, Caixa Postal 1524, 59072-970, Natal, RN (Brazil); Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP (Brazil); Brandt, F. T. [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP (Brazil); Carvalho, C. A. A. de; Fraga, E. S. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972, Rio de Janeiro, RJ (Brazil)
2010-09-15T23:59:59.000Z
We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field {phi}{sub c}, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schroedinger field representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle point for fixed boundary fields, which is the classical field {phi}{sub c}, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally reduced effective theory for the thermal system. We calculate the two-point correlation as an example.
Noncommutative deformations of quantum field theories, locality, and causality
Michael A. Soloviev
2010-12-16T23:59:59.000Z
We investigate noncommutative deformations of quantum field theories for different star products, particularly emphasizing the locality properties and the regularity of the deformed fields. Using functional analysis methods, we describe the basic structural features of the vacuum expectation values of star-modified products of fields and field commutators. As an alternative to microcausality, we introduce a notion of $\\theta$-locality, where $\\theta$ is the noncommutativity parameter. We also analyze the conditions for the convergence and continuity of star products and define the function algebra that is most suitable for the Moyal and Wick-Voros products. This algebra corresponds to the concept of strict deformation quantization and is a useful tool for constructing quantum field theories on a noncommutative space-time.
Quantum field theory in spaces with closed timelike curves
Boulware, D.G. (Department of Physics FM-15, University of Washington, Seattle, Washington 98195 (United States))
1992-11-15T23:59:59.000Z
Gott spacetime has closed timelike curves, but no locally anomalous stress energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2{pi}. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
"Einstein's Dream" - Quantum Mechanics as Theory of Classical Random Fields
Andrei Khrennikov
2012-04-22T23:59:59.000Z
This is an introductory chapter of the book in progress on quantum foundations and incompleteness of quantum mechanics. Quantum mechanics is represented as statistical mechanics of classical fields.
Quantum Field and Cosmic Field-Finite Geometrical Field Theory of Matter Motion Part Three
Jianhua Xiao
2005-12-20T23:59:59.000Z
This research establishes an operational measurement way to express the quantum field theory in a geometrical form. In four-dimensional spacetime continuum, the orthogonal rotation is defined. It forms two sets of equations: one set is geometrical equations, another set is the motion equations. The Lorentz transformation can be directly derived from the geometrical equations, and the proper time of general relativity is well expressed by time displacement field. By the motion equations, the typical time displacement field of matter motion is discussed. The research shows that the quantum field theory can be established based on the concept of orthogonal rotation. On this sense, the quantum matter motion in physics is viewed as the orthogonal rotation of spacetime continuum. In this paper, it shows that there are three typical quantum solutions. One is particle-like solution, one is generation-type solution, and one is pure wave type solution. For each typical solution, the force fields are different. Many features of quantum field can be well explained by this theoretic form. Finally, the general matter motion is discussed, the main conclusions are: (1). Geometrically, cosmic vacuum field can be described by the curvature spacetime; (2). The spatial deformation of planet is related with a planet electromagnetic field; (3). For electric charge less matter, the volume of matter will be expanding infinitely; (4).For strong electric charge matter, it shows that the volume of matter will be contracting infinitely.
Quantum Field Theory in de Sitter Universe: Ambient Space Formalism
Mohammad Vahid Takook
2014-09-03T23:59:59.000Z
Quantum field theory in the $4$-dimensional de Sitter space-time is constructed on a unique Bunch-Davies vacuum state in the ambient space formalism in a rigorous mathematical framework. This work is based on the group representation theory and the analyticity of the complexified pseudo-Riemannian manifolds. The unitary irreducible representations of de Sitter group and their corresponding Hilbert spaces are reformulated in the ambient space formalism. Defining the creation and annihilation operators, quantum field operators and their corresponding analytic two-point functions for various spin fields ($s=0,\\frac{1}{2},1,\\frac{3}{2}, 2$) have been constructed. The various spin massless fields can be constructed in terms of the massless conformally coupled scalar field in this formalism. Then the quantum massless minimally coupled scalar field operator, for the first time, is also constructed on Bunch-Davies vacuum state which preserve the analyticity. We show that the massless fields with $s\\leq 2$ can only propagate in de Sitter ambient space formalism. The massless gauge invariant field equations with $s=1, \\frac{3}{2}, 2$ are studied by using the gauge principle. The conformal quantum spin-$2$ field, based on the gauge gravity model, is studied. The gauge spin-$\\frac{3}{2}$ fields satisfy the Grassmannian algebra, and hence, naturally provoke one to couple them with the gauge spin-$2$ field and the super-algebra is automatically appeared. We conclude that the gravitational field may be constructed by three parts, namely, the de Sitter background, the gauge spin-$2$ field and the gauge spin-$\\frac{3}{2}$ field.
Test Functions Space in Noncommutative Quantum Field Theory
M. Chaichian; M. Mnatsakanova; A. Tureanu; Yu. Vernov
2008-07-26T23:59:59.000Z
It is proven that the $\\star$-product of field operators implies that the space of test functions in the Wightman approach to noncommutative quantum field theory is one of the Gel'fand-Shilov spaces $S^{\\beta}$ with $\\beta test functions smears the noncommutative Wightman functions, which are in this case generalized distributions, sometimes called hyperfunctions. The existence and determination of the class of the test function spaces in NC QFT is important for any rigorous treatment in the Wightman approach.
De Sitter Space, Interacting Quantum Field Theory And Alpha Vacua
Goldstein, K
2005-01-01T23:59:59.000Z
Inspired by recent evidence for a positive cosmological constant, this thesis considers some of the implications of trying to incorporate approximately seventy percent of the universe, namely dark energy, consistently into quantum field theory on a curved background. Such considerations may have implications for inflation, the understanding of dark energy at the present time and finally the challenging topic of trying to incorporate a positive cosmological constant into string theory. We will mainly examine various aspects of the one parameter family of de Sitter invariant states—the so called ?-vacua. On the phenomenological side, not only could such states provide a window into trans-planckian physics through their imprint on the cosmological microwave background (CMB), but they may also be a source of ultra-high energy cosmic rays (UHECR) at the present time. From a purely theoretical perspective, formulating interacting quantum field theory in these states is a challenging problem whic...
Noncommutative version of Borcherds' approach to quantum field theory
Christian Brouder; Nguyen Viet Dang; Alessandra Frabetti
2015-01-31T23:59:59.000Z
Richard Borcherds proposed an elegant geometric version of renormalized perturbative quantum field theory in curved spacetimes, where Lagrangians are sections of a Hopf algebra bundle over a smooth manifold. However, this framework looses its geometric meaning when Borcherds introduces a (graded) commutative normal product. We present a fully geometric version of Borcherds' quantization where the (external) tensor product plays the role of the normal product. We construct a noncommutative many-body Hopf algebra and a module over it which contains all the terms of the perturbative expansion and we quantize it to recover the expectation values of standard quantum field theory when the Hopf algebra fiber is (graded) cocommutative. This construction enables to the second quantize any theory described by a cocommutative Hopf algebra bundle.
Quantum field theory for condensation of bosons and fermions
De Souza, Adriano N.; Filho, Victo S. [Laboratorio de Fisica Teorica e Computacional (LFTC), Universidade Cruzeiro do Sul, 01506-000, Sao Paulo (Brazil)
2013-03-25T23:59:59.000Z
In this brief review, we describe the formalism of the quantum field theory for the analysis of the condensation phenomenon in bosonic systems, by considering the cases widely verified in laboratory of trapped gases as condensate states, either with attractive or with repulsive two-body interactions. We review the mathematical formulation of the quantum field theory for many particles in the mean-field approximation, by adopting contact interaction potential. We also describe the phenomenon of condensation in the case of fermions or the degenerate Fermi gas, also verified in laboratory in the crossover BEC-BCS limit. We explain that such a phenomenon, equivalent to the bosonic condensation, can only occur if we consider the coupling of particles in pairs behaving like bosons, as occurs in the case of Cooper's pairs in superconductivity.
Toward an axiomatic formulation of noncommutative quantum field theory
Chaichian, M.; Tureanu, A. [Department of Physics, University of Helsinki, P.O. Box 64, FIN-00014 Helsinki (Finland); Mnatsakanova, M. N. [Skobeltsyn Institute of Nuclear Physics, Moscow State University, 119992 Vorobyevy Gory, Moscow (Russian Federation); Nishijima, K. [Department of Physics, University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan); Vernov, Yu. S. [Institute for Nuclear Research, Russian Academy of Sciences, 60th October Anniversary prospect 7a, 117312 Moscow (Russian Federation)
2011-03-15T23:59:59.000Z
We propose new Wightman functions as vacuum expectation values of products of field operators in the noncommutative space-time. These Wightman functions involve the *-product among the fields, compatible with the twisted Poincare symmetry of the noncommutative quantum field theory (NC QFT). In the case of only space-space noncommutativity ({theta}{sub 0i}= 0), we prove the CPT theorem using the noncommutative form of the Wightman functions. We also show that the spin-statistics theorem, demonstrated for the simplest case of a scalar field, holds in NC QFT within this formalism.
Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes
Alexander Schenkel
2012-10-03T23:59:59.000Z
The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of the usual symmetry reduction procedure to noncommutative gravity. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models. In part two we develop a new formalism for quantum field theory on noncommutative curved spacetimes by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. We also study explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories. The convergent deformation of simple toy models is investigated and it is found that these theories have an improved behaviour at short distances, i.e. in the ultraviolet. In part three we study homomorphisms between and connections on noncommutative vector bundles. We prove that all homomorphisms and connections of the deformed theory can be obtained by applying a quantization isomorphism to undeformed homomorphisms and connections. The extension of homomorphisms and connections to tensor products of bimodules is clarified. As a nontrivial application of the new mathematical formalism we extend our studies of exact noncommutative gravity solutions to more general deformations.
Perturbative quantum field theory in the framework of the fermionic projector
Finster, Felix, E-mail: finster@ur.de [Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg (Germany)] [Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg (Germany)
2014-04-15T23:59:59.000Z
We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.
Negative-frequency modes in quantum field theory
Dickinson, Robert; Millington, Peter
2015-01-01T23:59:59.000Z
We consider a departure from standard quantum field theory, constructed so as to permit momentum eigenstates of both positive and negative energy. The resulting theory is intriguing because it brings about the cancellation of leading ultra-violet divergences and the absence of a zero-point energy. The theory gives rise to tree-level source-to-source transition amplitudes that are manifestly causal and consistent with standard S-matrix elements. It also leads to the usual result for the oblique corrections to the standard electroweak theory. Remarkably, the latter agreement relies on the breakdown of naive perturbation theory due to resonance effects. It remains to be shown that there are no problems with perturbative unitarity.
Negative-frequency modes in quantum field theory
Robert Dickinson; Jeff Forshaw; Peter Millington
2015-03-06T23:59:59.000Z
We consider a departure from standard quantum field theory, constructed so as to permit momentum eigenstates of both positive and negative energy. The resulting theory is intriguing because it brings about the cancellation of leading ultra-violet divergences and the absence of a zero-point energy. The theory gives rise to tree-level source-to-source transition amplitudes that are manifestly causal and consistent with standard S-matrix elements. It also leads to the usual result for the oblique corrections to the standard electroweak theory. Remarkably, the latter agreement relies on the breakdown of naive perturbation theory due to resonance effects. It remains to be shown that there are no problems with perturbative unitarity.
Multi-time wave functions for quantum field theory
Petrat, Sören, E-mail: petrat@math.lmu.de [Mathematisches Institut, Ludwig-Maximilians-Universität, Theresienstr. 39, 80333 München (Germany); Tumulka, Roderich, E-mail: tumulka@math.rutgers.edu [Department of Mathematics, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019 (United States)
2014-06-15T23:59:59.000Z
Multi-time wave functions such as ?(t{sub 1},x{sub 1},…,t{sub N},x{sub N}) have one time variable t{sub j} for each particle. This type of wave function arises as a relativistic generalization of the wave function ?(t,x{sub 1},…,x{sub N}) of non-relativistic quantum mechanics. We show here how a quantum field theory can be formulated in terms of multi-time wave functions. We mainly consider a particular quantum field theory that features particle creation and annihilation. Starting from the particle–position representation of state vectors in Fock space, we introduce multi-time wave functions with a variable number of time variables, set up multi-time evolution equations, and show that they are consistent. Moreover, we discuss the relation of the multi-time wave function to two other representations, the Tomonaga–Schwinger representation and the Heisenberg picture in terms of operator-valued fields on space–time. In a certain sense and under natural assumptions, we find that all three representations are equivalent; yet, we point out that the multi-time formulation has several technical and conceptual advantages. -- Highlights: •Multi-time wave functions are manifestly Lorentz-covariant objects. •We develop consistent multi-time equations with interaction for quantum field theory. •We discuss in detail a particular model with particle creation and annihilation. •We show how multi-time wave functions are related to the Tomonaga–Schwinger approach. •We show that they have a simple representation in terms of operator valued fields.
Ioannis P. Zois
2014-01-16T23:59:59.000Z
We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT) and Noncommutative Floer Homology (NCFH). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that NCTQFT is the correct mathematical framework for a quantum field theory of all known interactions in nature (including gravity). On the other hand we hope that a possible NCFH will apply to practically every 3-manifold (and not only to homology 3-spheres as ordinary Floer Homology currently does). The two motivations are closely related since, at least in the commutative case, Floer Homology Groups constitute the space of quantum observables of (3+1)-dim Topological Quantum Field Theory. Towards this goal we present some "Noncommutative" Versions of Hodge Theory for noncommutative differentail forms and tangential cohomology for foliations.
Multi-scale quantum simulation of quantum field theory using wavelets
Gavin K. Brennen; Peter Rohde; Barry C. Sanders; Sukhwinder Singh
2014-12-02T23:59:59.000Z
A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field degrees of freedom in a wavelet basis---a multi-scale description of the theory. Since wavelets are compact wavefunctions, this encoding allows for quantum simulations to create particle excitations with compact support and provides a natural way to associate observables in the theory to finite resolution detectors. We show that the wavelet basis is well suited to compute subsystem entanglement entropy by dividing the field into contributions from short-range wavelet degrees of freedom and long-range scale degrees of freedom, of which the latter act as renormalized modes which capture the essential physics at a renormalization fixed point.
Construction of Quantum Field Theories with Factorizing S-Matrices
Gandalf Lechner
2007-02-12T23:59:59.000Z
A new approach to the construction of interacting quantum field theories on two-dimensional Minkowski space is discussed. In this program, models are obtained from a prescribed factorizing S-matrix in two steps. At first, quantum fields which are localized in infinitely extended, wedge-shaped regions of Minkowski space are constructed explicitly. In the second step, local observables are analyzed with operator-algebraic techniques, in particular by using the modular nuclearity condition of Buchholz, d'Antoni and Longo. Besides a model-independent result regarding the Reeh-Schlieder property of the vacuum in this framework, an infinite class of quantum field theoretic models with non-trivial interaction is constructed. This construction completes a program initiated by Schroer in a large family of theories, a particular example being the Sinh-Gordon model. The crucial problem of establishing the existence of local observables in these models is solved by verifying the modular nuclearity condition, which here amounts to a condition on analytic properties of form factors of observables localized in wedge regions. It is shown that the constructed models solve the inverse scattering problem for the considered class of S-matrices. Moreover, a proof of asymptotic completeness is obtained by explicitly computing total sets of scattering states. The structure of these collision states is found to be in agreement with the heuristic formulae underlying the Zamolodchikov-Faddeev algebra.
Noncommutative Common Cause Principles in algebraic quantum field theory
Hofer-Szabo, Gabor [Research Center for the Humanities, Budapest (Hungary)] [Research Center for the Humanities, Budapest (Hungary); Vecsernyes, Peter [Wigner Research Centre for Physics, Budapest (Hungary)] [Wigner Research Centre for Physics, Budapest (Hungary)
2013-04-15T23:59:59.000Z
States in algebraic quantum field theory 'typically' establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V{sub A} and V{sub B}, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V{sub A} and V{sub B} and the set {l_brace}C, C{sup Up-Tack }{r_brace} screens off the correlation between A and B.
Untwisting Noncommutative R^d and the Equivalence of Quantum Field Theories
Robert Oeckl
2000-03-13T23:59:59.000Z
We show that there is a duality exchanging noncommutativity and non-trivial statistics for quantum field theory on R^d. Employing methods of quantum groups, we observe that ordinary and noncommutative R^d are related by twisting. We extend the twist to an equivalence for quantum field theory using the framework of braided quantum field theory. The twist exchanges both commutativity with noncommutativity and ordinary with non-trivial statistics. The same holds for the noncommutative torus.
Towards quantum noncommutative {kappa}-deformed field theory
Daszkiewicz, Marcin; Lukierski, Jerzy; Woronowicz, Mariusz [Institute of Theoretical Physics, University of Wroclaw pl. Maxa Borna 9, 50-206 Wroclaw (Poland)
2008-05-15T23:59:59.000Z
We introduce a new {kappa}-star product describing the multiplication of quantized {kappa}-deformed free fields. The {kappa} deformation of local free quantum fields originates from two sources: noncommutativity of space-time and the {kappa} deformation of field oscillators algebra; we relate these two deformations. We demonstrate that for a suitable choice of {kappa}-deformed field oscillators algebra, the {kappa}-deformed version of the microcausality condition is satisfied, and it leads to the deformation of the Pauli-Jordan commutation function defined by the {kappa}-deformed mass shell. We show by constructing the {kappa}-deformed Fock space that the use of the {kappa}-deformed oscillator algebra permits one to preserve the bosonic statistics of n-particle states. The proposed star product is extended to the product of n fields, which for n=4 defines the interaction vertex in perturbative description of the noncommutative quantum {lambda}{phi}{sup 4} field theory. It appears that the classical four-momentum conservation law is satisfied at the interaction vertices.
Group field theory formulation of 3d quantum gravity coupled to matter fields
Daniele Oriti; James Ryan
2006-02-02T23:59:59.000Z
We present a new group field theory describing 3d Riemannian quantum gravity coupled to matter fields for any choice of spin and mass. The perturbative expansion of the partition function produces fat graphs colored with SU(2) algebraic data, from which one can reconstruct at once a 3-dimensional simplicial complex representing spacetime and its geometry, like in the Ponzano-Regge formulation of pure 3d quantum gravity, and the Feynman graphs for the matter fields. The model then assigns quantum amplitudes to these fat graphs given by spin foam models for gravity coupled to interacting massive spinning point particles, whose properties we discuss.
Inequivalence of quantum field theories on noncommutative spacetimes: Moyal versus Wick-Voros planes
Balachandran, A. P. [Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (United States); Departamento de Matematicas, Universidad Carlos III de Madrid, 28911 Leganes, Madrid (Spain); Ibort, A. [Departamento de Matematicas, Universidad Carlos III de Madrid, 28911 Leganes, Madrid (Spain); Marmo, G. [Dipartimento di Scienze Fisiche, University of Napoli and INFN, Via Cinthia I-80126 Napoli (Italy); Martone, M. [Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (United States); Dipartimento di Scienze Fisiche, University of Napoli and INFN, Via Cinthia I-80126 Napoli (Italy)
2010-04-15T23:59:59.000Z
In this paper, we further develop the analysis started in an earlier paper on the inequivalence of certain quantum field theories on noncommutative spacetimes constructed using twisted fields. The issue is of physical importance. Thus it is well known that the commutation relations among spacetime coordinates, which define a noncommutative spacetime, do not constrain the deformation induced on the algebra of functions uniquely. Such deformations are all mathematically equivalent in a very precise sense. Here we show how this freedom at the level of deformations of the algebra of functions can fail on the quantum field theory side. In particular, quantum field theory on the Wick-Voros and Moyal planes are shown to be inequivalent in a few different ways. Thus quantum field theory calculations on these planes will lead to different physics even though the classical theories are equivalent. This result is reminiscent of chiral anomaly in gauge theories and has obvious physical consequences. The construction of quantum field theories on the Wick-Voros plane has new features not encountered for quantum field theories on the Moyal plane. In fact it seems impossible to construct a quantum field theory on the Wick-Voros plane which satisfies all the properties needed of field theories on noncommutative spaces. The Moyal twist seems to have unique features which make it a preferred choice for the construction of a quantum field theory on a noncommutative spacetime.
Matter-enhanced transition probabilities in quantum field theory
Ishikawa, Kenzo, E-mail: ishikawa@particle.sci.hokudai.ac.jp; Tobita, Yutaka
2014-05-15T23:59:59.000Z
The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincaré transformation. The ground state, vacuum, is singlet and one particle states are transformed as elements of irreducible representation of the group. The covariant one particles are momentum eigenstates expressed by plane waves and extended in space. Although the S-matrix defined with initial and final states of these states hold the symmetries and are applied to isolated states, out-going states for the amplitude of the event that they are detected at a finite-time interval T in experiments are expressed by microscopic states that they interact with, and are surrounded by matters in detectors and are not plane waves. These matter-induced effects modify the probabilities observed in realistic situations. The transition amplitudes and probabilities of the events are studied with the S-matrix, S[T], that satisfies the boundary condition at T. Using S[T], the finite-size corrections of the form of 1/T are found. The corrections to Fermi’s golden rule become larger than the original values in some situations for light particles. They break Lorentz invariance even in high energy region of short de Broglie wave lengths. -- Highlights: •S-matrix S[T] for the finite-time interval in relativistic field theory. •S[T] satisfies the boundary condition and gives correction of 1/T . •The large corrections for light particles breaks Lorentz invariance. •The corrections have implications to neutrino experiments.
Embedding quantum and random optics in a larger field theory
Peter Morgan
2008-06-09T23:59:59.000Z
Introducing creation and annihilation operators for negative frequency components extends the algebra of smeared local observables of quantum optics to include an associated classical random field optics.
Two studies of topological quantum field theory in two dimensions
Lin, Haijian Kevin
2012-01-01T23:59:59.000Z
56] G. Segal. The definition of conformal field theory. In:ABELIAN GAUGE THEORY IN FAMILIES Definition 2.4.1. Let 0 ? wOF ABELIAN GAUGE THEORY IN FAMILIES Definition 2.2.6. Recall
Why Renormalizable NonCommutative Quantum Field Theories?
Vincent Rivasseau
2007-11-12T23:59:59.000Z
We complete our previous recent review on noncommutative field theory, discussing in particular the constructive aproach to the Grosse-Wulkenhaar theory. We also suggest that by gluing together many Grosse-Wulkenhaar theories at high energy one can obtain an effective commutative field theory at lower energy.
Green function identities in Euclidean quantum field theory
G. Sardanashvily
2006-04-01T23:59:59.000Z
Given a generic Lagrangian system of even and odd fields, we show that any infinitesimal transformation of its classical Lagrangian yields the identities which Euclidean Green functions of quantum fields satisfy.
Brane Dynamics and Four-Dimensional Quantum Field Theory
N. D. Lambert; P. C. West
1998-11-19T23:59:59.000Z
We review the relation between the classical dynamics of the M-fivebrane and the quantum low energy effective action for N=2 Yang-Mills theories. We also discuss some outstanding issues in this correspondence.
Quantum Space-Time and Noncommutative Gauge Field Theories
Sami Saxell
2009-09-17T23:59:59.000Z
The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative space-time is the apparent loss of Lorentz invariance that has been addressed in different ways in the literature. One recently developed approach is to eliminate the Lorentz violating effects by integrating over the parameter of noncommutativity. Fundamental properties of such theories are investigated in this thesis. Another issue addressed is model building, which is difficult in the noncommutative setting due to severe restrictions on the possible gauge symmetries imposed by the noncommutativity of the space-time. Possible ways to relieve these restrictions are investigated and applied and a noncommutative version of the Minimal Supersymmetric Standard Model is presented. While putting the results obtained in the three original publications into their proper context, the introductory part of this thesis aims to provide an overview of the present situation in the field.
UV/IR duality in noncommutative quantum field theory
Andre Fischer; Richard J. Szabo
2010-06-16T23:59:59.000Z
We review the construction of renormalizable noncommutative euclidean phi(4)-theories based on the UV/IR duality covariant modification of the standard field theory, and how the formalism can be extended to scalar field theories defined on noncommutative Minkowski space.
On general properties of Lorentz invariant formulation of noncommutative quantum field theory
Sami Saxell
2008-08-19T23:59:59.000Z
We study general properties of certain Lorentz invariant noncommutative quantum field theories proposed in the literature. We show that causality in those theories does not hold, in contrast to the canonical noncommutative field theory with the light-wedge causality condition. This is the consequence of the infinite nonlocality of the theory getting spread in all spacetime directions. We also show that the time-ordered perturbation theory arising from the Hamiltonian formulation of noncommutative quantum field theories remains inequivalent to the covariant perturbation theory with usual Feynman rules even after restoration of Lorentz symmetry.
Quantum Field Theory on the Noncommutative Plane with $E_q(2)$ Symmetry
M. Chaichian; A. Demichev; P. Presnajder
1999-04-20T23:59:59.000Z
We study properties of a scalar quantum field theory on the two-dimensional noncommutative plane with $E_q(2)$ quantum symmetry. We start from the consideration of a firstly quantized quantum particle on the noncommutative plane. Then we define quantum fields depending on noncommutative coordinates and construct a field theoretical action using the $E_q(2)$-invariant measure on the noncommutative plane. With the help of the partial wave decomposition we show that this quantum field theory can be considered as a second quantization of the particle theory on the noncommutative plane and that this field theory has (contrary to the common belief) even more severe ultraviolet divergences than its counterpart on the usual commutative plane. Finally, we introduce the symmetry transformations of physical states on noncommutative spaces and discuss them in detail for the case of the $E_q(2)$ quantum group.
Dynamo in Helical MHD Turbulence: Quantum Field Theory Approach
M. Hnatic; M. Jurcisin; M. Stehlik
2006-03-10T23:59:59.000Z
A quantum field model of helical MHD stochastically forced by gaussian hydrodynamic, magnetic and mixed noices is investigated. These helical noises lead to an exponential increase of magnetic fluctuations in the large scale range. Instabilities, which are produced in this process, are eliminated by spontaneous symmetry breaking mechanism accompanied by creation of the homogeneous stationary magnetic field.
Lessons for Loop Quantum Gravity from Parametrised Field Theory
Thomas Thiemann
2010-10-12T23:59:59.000Z
In a series of seminal papers, Laddha and Varadarajan have developed in depth the quantisation of Parametrised Field Theory (PFT) in the kind of discontinuous representations that are employed in Loop Quantum Gravity (LQG). In one spatial dimension (circle) PFT is very similar to the closed bosonic string and the constraint algebra is isomorphic to two mutually commuting Witt algebras. Its quantisation is therefore straightforward in LQG like representations which by design lead to non anomalous, unitary, albeit discontinuous representations of the spatial diffeomorphism group. In particular, the complete set of (distributional) solutions to the quantum constraints, a preferred and complete algebra of Dirac observables and the associated physical inner product has been constructed. On the other hand, the two copies of Witt algebras are classically isomorphic to the Dirac or hypersurface deformation algebra of General Relativity (although without structure functions). The question we address in this paper, also raised by Laddha and Varadarajan in their paper, is whether we can quantise the Dirac algebra in such a way that its space of distributional solutions coincides with the one just described. This potentially teaches us something about LQG where a classically equivalent formulation of the Dirac algebra in terms of spatial diffeomorphism Lie algebras is not at our disposal. We find that, in order to achieve this, the Hamiltonian constraint has to be quantised by methods that extend those previously considered. The amount of quantisation ambiguities is somewhat reduced but not eliminated. We also show that the algebra of Hamiltonian constraints closes in a precise sense, with soft anomalies, that is, anomalies that do not cause inconsistencies. We elaborate on the relevance of these findings for full LQG.
Kossow, Marcel [I. Institut fuer Theoretische Physik, Universitaet Hamburg, Jungiusstrasse 9, D - 20355 Hamburg (Germany)
2008-03-15T23:59:59.000Z
An energy correction is calculated in the time-independent perturbation setup using a regularized ultraviolet finite Hamiltonian on the noncommutative Minkowski space. The correction to the energy is invariant under rotation and translation but is not Lorentz covariant, and this leads to a distortion of the dispersion relation. In the limit where the noncommutativity vanishes, the common quantum field theory on the commutative Minkowski space is reobtained. The calculations are restricted to the regularized cubic interaction.
Miransky, Vladimir A
2015-01-01T23:59:59.000Z
A range of quantum field theoretical phenomena driven by external magnetic fields and their applications in relativistic systems and quasirelativistic condensed matter ones, such as graphene and Dirac/Weyl semimetals, are reviewed. We start by introducing the underlying physics of the magnetic catalysis. The dimensional reduction of the low-energy dynamics of relativistic fermions in an external magnetic field is explained and its role in catalyzing spontaneous symmetry breaking is emphasized. The general theoretical consideration is supplemented by the analysis of the magnetic catalysis in quantum electrodynamics, chromodynamics and quasirelativistic models relevant for condensed matter physics. By generalizing the ideas of the magnetic catalysis to the case of nonzero density and temperature, we argue that other interesting phenomena take place. The chiral magnetic and chiral separation effects are perhaps the most interesting among them. In addition to the general discussion of the physics underlying chira...
Quantum field theory in curved spacetime, the operator product expansion, and dark energy
S. Hollands; R. M. Wald
2008-05-22T23:59:59.000Z
To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved spacetime, the theory must be formulated in a local and covariant manner in terms of locally measureable field observables. Since a generic curved spacetime does not possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require symmetries or a preferred notion of a ``vacuum state'' and ``particles''. We propose such a formulation of quantum field theory, wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients--and, thus, the quantum field theory. By contrast, ground/vacuum states--in spacetimes, such as Minkowski spacetime, where they may be defined--cannot vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than the natural scales of the theory.
Vladimir A. Miransky; Igor A. Shovkovy
2015-03-02T23:59:59.000Z
A range of quantum field theoretical phenomena driven by external magnetic fields and their applications in relativistic systems and quasirelativistic condensed matter ones, such as graphene and Dirac/Weyl semimetals, are reviewed. We start by introducing the underlying physics of the magnetic catalysis. The dimensional reduction of the low-energy dynamics of relativistic fermions in an external magnetic field is explained and its role in catalyzing spontaneous symmetry breaking is emphasized. The general theoretical consideration is supplemented by the analysis of the magnetic catalysis in quantum electrodynamics, chromodynamics and quasirelativistic models relevant for condensed matter physics. By generalizing the ideas of the magnetic catalysis to the case of nonzero density and temperature, we argue that other interesting phenomena take place. The chiral magnetic and chiral separation effects are perhaps the most interesting among them. In addition to the general discussion of the physics underlying chiral magnetic and separation effects, we also review their possible phenomenological implications in heavy-ion collisions and compact stars. We also discuss the application of the magnetic catalysis ideas for the description of the quantum Hall effect in monolayer and bilayer graphene, and conclude that the generalized magnetic catalysis, including both the magnetic catalysis condensates and the quantum Hall ferromagnetic ones, lies at the basis of this phenomenon. We also consider how an external magnetic field affects the underlying physics in a class of three-dimensional quasirelativistic condensed matter systems, Dirac semimetals. While at sufficiently low temperatures and zero density of charge carriers, such semimetals are expected to reveal the regime of the magnetic catalysis, the regime of Weyl semimetals with chiral asymmetry is realized at nonzero density...
Vladimir A. Miransky; Igor A. Shovkovy
2015-04-10T23:59:59.000Z
A range of quantum field theoretical phenomena driven by external magnetic fields and their applications in relativistic systems and quasirelativistic condensed matter ones, such as graphene and Dirac/Weyl semimetals, are reviewed. We start by introducing the underlying physics of the magnetic catalysis. The dimensional reduction of the low-energy dynamics of relativistic fermions in an external magnetic field is explained and its role in catalyzing spontaneous symmetry breaking is emphasized. The general theoretical consideration is supplemented by the analysis of the magnetic catalysis in quantum electrodynamics, chromodynamics and quasirelativistic models relevant for condensed matter physics. By generalizing the ideas of the magnetic catalysis to the case of nonzero density and temperature, we argue that other interesting phenomena take place. The chiral magnetic and chiral separation effects are perhaps the most interesting among them. In addition to the general discussion of the physics underlying chiral magnetic and separation effects, we also review their possible phenomenological implications in heavy-ion collisions and compact stars. We also discuss the application of the magnetic catalysis ideas for the description of the quantum Hall effect in monolayer and bilayer graphene, and conclude that the generalized magnetic catalysis, including both the magnetic catalysis condensates and the quantum Hall ferromagnetic ones, lies at the basis of this phenomenon. We also consider how an external magnetic field affects the underlying physics in a class of three-dimensional quasirelativistic condensed matter systems, Dirac semimetals. While at sufficiently low temperatures and zero density of charge carriers, such semimetals are expected to reveal the regime of the magnetic catalysis, the regime of Weyl semimetals with chiral asymmetry is realized at nonzero density...
Wick rotation for quantum field theories on degenerate Moyal space(-time)
Grosse, Harald; Lechner, Gandalf [Department of Physics, University of Vienna, 1090 Vienna (Austria)] [Department of Physics, University of Vienna, 1090 Vienna (Austria); Ludwig, Thomas [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig (Germany) [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig (Germany); Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany); Verch, Rainer [Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)] [Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)
2013-02-15T23:59:59.000Z
In this paper the connection between quantum field theories on flat noncommutative space(-times) in Euclidean and Lorentzian signature is studied for the case that time is still commutative. By making use of the algebraic framework of quantum field theory and an analytic continuation of the symmetry groups which are compatible with the structure of Moyal space, a general correspondence between field theories on Euclidean space satisfying a time zero condition and quantum field theories on Moyal Minkowski space is presented ('Wick rotation'). It is then shown that field theories transferred to Moyal space(-time) by Rieffel deformation and warped convolution fit into this framework, and that the processes of Wick rotation and deformation commute.
Wen, Xiao-Gang
The projective construction is a powerful approach to deriving the bulk and edge field theories of non-Abelian fractional quantum Hall (FQH) states and yields an understanding of non-Abelian FQH states in terms of the ...
Counting degrees of freedom in quantum field theory using entanglement entropy
Mezei, Márk (Márk Koppany)
2014-01-01T23:59:59.000Z
We devote this thesis to the exploration of how to define the number of degrees of freedom in quantum field theory. Intuitively, the number of degrees of freedom should decrease along the renormalization group (RG) flow, ...
B. Julia-Diaz; H. Kamano; T. -S. H. Lee; A. Matsuyama; T. Sato; N. Suzuki
2009-02-18T23:59:59.000Z
Within the relativistic quantum field theory, we analyze the differences between the $\\pi N$ reaction models constructed from using (1) three-dimensional reductions of Bethe-Salpeter Equation, (2) method of unitary transformation, and (3) time-ordered perturbation theory. Their relations with the approach based on the dispersion relations of S-matrix theory are dicusssed.
An Interpretation of Noncommutative Field Theory in Terms of a Quantum Shift
M. Chaichian; K. Nishijima; A. Tureanu
2005-11-08T23:59:59.000Z
Noncommutative coordinates are decomposed into a sum of geometrical ones and a universal quantum shift operator. With the help of this operator, the mapping of a commutative field theory into a noncommutative field theory (NCFT) is introduced. A general measure for the Lorentz-invariance violation in NCFT is also derived.
Quantum motion equation and Poincare translation invariance of noncommutative field theory
Zheng Ze Ma
2006-03-16T23:59:59.000Z
We study the Moyal commutators and their expectation values between vacuum states and non-vacuum states for noncommutative scalar field theory. For noncommutative $\\phi^{\\star4}$ scalar field theory, we derive its energy-momentum tensor from translation transformation and Lagrange field equation. We generalize the Heisenberg and quantum motion equations to the form of Moyal star-products for noncommutative $\\phi^{\\star4}$ scalar field theory for the case $\\theta^{0i}=0$ of spacetime noncommutativity. Then we demonstrate the Poincar{\\' e} translation invariance for noncommutative $\\phi^{\\star4}$ scalar field theory for the case $\\theta^{0i}=0$ of spacetime noncommutativity.
On Conformal Field Theory and Number Theory
Huang, An
2011-01-01T23:59:59.000Z
Frontiers in Number Theory, Physics, and Ge- ometry II. (Witten, Quantum Field Theory, Crassmannians, and AlgebraicJ. Polchinski, String Theory, Vol. 1, Cambridge Univ.
Introduction Classical Field Theory
Baer, Christian
Introduction Classical Field Theory Locally Covariant Quantum Field Theory Renormalization Time evolution Conclusions and outlook Locality and Algebraic Structures in Field Theory Klaus Fredenhagen IIÂ¨utsch and Pedro Lauridsen Ribeiro) Klaus Fredenhagen Locality and Algebraic Structures in Field Theory #12
V. P. Neznamov
2015-02-02T23:59:59.000Z
The paper presents the representation of quantum field theory without introduction of infinity bare masses and coupling constants of fermions. Counter-terms, compensating for divergent quantities in self-energy diagrams of fermions and vacuum polarization diagrams at all orders of the perturbation theory, appear in the appropriate Hamiltonians under the special time-dependent unitary transformation.
Failure of microcausality in quantum field theory on noncommutative spacetime
Greenberg, O.W. [High Energy Physics Division, Department of Physical Sciences, University of Helsinki, FIN-00014, Helsinki (Finland)
2006-02-15T23:59:59.000Z
The commutator of ratio {phi}(x)*{phi}(x) ratio with {partial_derivative}{sub {mu}}{sup y} ratio {phi}(y)*{phi}(y) ratio fails to vanish at equal times and thus also fails to obey microcausality at spacelike separation even for the case in which {theta}{sup 0i}=0. The failure to obey microcausality for these sample observables implies that this form of noncommutative field theory fails to obey microcausality in general. This result holds generally when there are time derivatives in the observables. We discuss possible responses to this problem.
Matteo Villani
2009-07-28T23:59:59.000Z
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not contemplated by this function. Within this scheme, quantum mechanics, classical field theory and a quantum theory for scalar fields are discussed. As a by-product of the probabilistic scheme for classical field theory, the equations of the De Donder-Weyl theory for multi-dimensional variational problems are recovered.
Parallelism of quantum computations from prequantum classical statistical field theory (PCSFT)
Andrei Khrennikov
2008-03-10T23:59:59.000Z
This paper is devoted to such a fundamental problem of quantum computing as quantum parallelism. It is well known that quantum parallelism is the basis of the ability of quantum computer to perform in polynomial time computations performed by classical computers for exponential time. Therefore better understanding of quantum parallelism is important both for theoretical and applied research, cf. e.g. David Deutsch \\cite{DD}. We present a realistic interpretation based on recently developed prequantum classical statistical field theory (PCSFT). In the PCSFT-approach to QM quantum states (mixed as well as pure) are labels of special ensembles of classical fields. Thus e.g. a single (!) ``electron in the pure state'' $\\psi$ can be identified with a special `` electron random field,'' say $\\Phi_\\psi(\\phi).$ Quantum computer operates with such random fields. By one computational step for e.g. a Boolean function $f(x_1,...,x_n)$ the initial random field $\\Phi_{\\psi_0}(\\phi)$ is transformed into the final random field $\\Phi_{\\psi_f}(\\phi)$ ``containing all values'' of $f.$ This is the objective of quantum computer's ability to operate quickly with huge amounts of information -- in fact, with classical random fields.
Quantum field theory solution for a short-range interacting SO(3) quantum spin-glass
C. M. S. da Conceição; E. C. Marino
2009-03-02T23:59:59.000Z
We study the quenched disordered magnetic system, which is obtained from the 2D SO(3) quantum Heisenberg model, on a square lattice, with nearest neighbors interaction, by taking a Gaussian random distribution of couplings centered in an antiferromagnetic coupling, $\\bar J>0$ and with a width $\\Delta J$. Using coherent spin states we can integrate over the random variables and map the system onto a field theory, which is a generalization of the SO(3) nonlinear sigma model with different flavors corresponding to the replicas, coupling parameter proportional to $\\bar J$ and having a quartic spin interaction proportional to the disorder ($\\Delta J$). After deriving the CP$^1$ version of the system, we perform a calculation of the free energy density in the limit of zero replicas, which fully includes the quantum fluctuations of the CP$^1$ fields $z_i$. We, thereby obtain the phase diagram of the system in terms of ($T, \\bar J, \\Delta J$). This presents an ordered antiferromagnetic (AF) phase, a paramagnetic (PM) phase and a spin-glass (SG) phase. A critical curve separating the PM and SG phases ends at a quantum critical point located between the AF and SG phases, at T=0. The Edwards-Anderson order parameter, as well as the magnetic susceptibilities are explicitly obtained in each of the three phases as a function of the three control parameters. The magnetic susceptibilities show a Curie-type behavior at high temperatures and exhibit a clear cusp, characteristic of the SG transition, at the transition line. The thermodynamic stability of the phases is investigated by a careful analysis of the Hessian matrix of the free energy. We show that all principal minors of the Hessian are positive in the limit of zero replicas, implying in particular that the SG phase is stable.
A new look at the problem of gauge invariance in quantum field theory
Dan Solomon
2007-06-19T23:59:59.000Z
Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in order to obtain a physically correct result. In this paper we will examine this problem and determine why a theory that is supposed to be gauge invariant produces non-gauge invariant results.
Exact Amplitude-Based Resummation in Quantum Field Theory: Recent Results
Ward, B F L
2012-01-01T23:59:59.000Z
We present the current status of the application of our approach of exact amplitude-based resummation in quantum field theory to two areas of investigation: precision QCD calculations of all three of us as needed for LHC physics and the resummed quantum gravity realization by one of us (B.F.L.W.) of Feynman's formulation of Einstein's theory of general relativity. We discuss recent results as they relate to experimental observations. There is reason for optimism in the attendant comparison of theory and experiment.
Achim Kempf; David M. Jackson; Alejandro H. Morales
2014-09-23T23:59:59.000Z
We derive new all-purpose methods that involve the Dirac Delta distribution. Some of the new methods use derivatives in the argument of the Dirac Delta. We highlight potential avenues for applications to quantum field theory and we also exhibit a connection to the problem of blurring/deblurring in signal processing. We find that blurring, which can be thought of as a result of multi-path evolution, is, in Euclidean quantum field theory without spontaneous symmetry breaking, the strong coupling dual of the usual small coupling expansion in terms of the sum over Feynman graphs.
Gravity Dual for Reggeon Field Theory and Non-linear Quantum Finance
Yu Nakayama
2009-06-23T23:59:59.000Z
We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the non-relativistic conformal invariance. We discuss applications to scaling regime of Reggeon field theory and non-linear quantum finance. These theories possess scale invariance but may or may not break the conformal invariance, depending on the underlying symmetry assumptions.
Washington Taylor
2006-06-28T23:59:59.000Z
This elementary introduction to string field theory highlights the features and the limitations of this approach to quantum gravity as it is currently understood. String field theory is a formulation of string theory as a field theory in space-time with an infinite number of massive fields. Although existing constructions of string field theory require expanding around a fixed choice of space-time background, the theory is in principle background-independent, in the sense that different backgrounds can be realized as different field configurations in the theory. String field theory is the only string formalism developed so far which, in principle, has the potential to systematically address questions involving multiple asymptotically distinct string backgrounds. Thus, although it is not yet well defined as a quantum theory, string field theory may eventually be helpful for understanding questions related to cosmology in string theory.
Quantum Field Theory on Noncommutative Space-Times and the Persistence of Ultraviolet Divergences
M. Chaichian; A. Demichev; P. Presnajder
1999-04-13T23:59:59.000Z
We study properties of a scalar quantum field theory on two-dimensional noncommutative space-times. Contrary to the common belief that noncommutativity of space-time would be a key to remove the ultraviolet divergences, we show that field theories on a noncommutative plane with the most natural Heisenberg-like commutation relations among coordinates or even on a noncommutative quantum plane with $E_q(2)$-symmetry have ultraviolet divergences, while the theory on a noncommutative cylinder is ultraviolet finite. Thus, ultraviolet behaviour of a field theory on noncommutative spaces is sensitive to the topology of the space-time, namely to its compactness. We present general arguments for the case of higher space-time dimensions and as well discuss the symmetry transformations of physical states on noncommutative space-times.
1. P1,P2 (P1), (P2) Relativistic Quantum Field Theory
1. P1,P2 (P1), (P2) 2. 3. P1 4. P2 1 #12;P1 P2 " " Relativistic Quantum Field Theory Dirac 212p s1 212s QED 232p 212p s1 212s 232p #12;7 2009 2010 2S 2010 2011 2012 #12;8 2009 2010://tabletop.icepp.s.u- tokyo.ac.jp/Tabletop_experiments/HFS_measurement_with _quantum_oscillation.html P2(?) P1 #12
Quantum field theory in spaces with closed time-like curves
Boulware, D.G.
1992-12-31T23:59:59.000Z
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27{pi}. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Quantum field theory in spaces with closed time-like curves. [Gott space
Boulware, D.G.
1992-01-01T23:59:59.000Z
Gott spacetime has closed timelike curves, but no locally anomalous stress-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27[pi]. A scalar quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The stress tensor of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the stress tensor is regular and cannot prevent the formation of the Cauchy horizon.
Einstein-Podolsky-Rosen correlations of Dirac particles - quantum field theory approach
Pawel Caban; Jakub Rembielinski
2006-12-15T23:59:59.000Z
We calculate correlation function in the Einstein--Podolsky--Rosen type of experiment with massive relativistic Dirac particles in the framework of the quantum field theory formalism. We perform our calculations for states which are physically interesting and transforms covariantly under the full Lorentz group action, i.e. for pseudoscalar and vector state.
Tree Unitarity and Partial Wave Expansion in Noncommutative Quantum Field Theory
M. Chaichian; C. Montonen; A. Tureanu
2003-05-28T23:59:59.000Z
The validity of the tree-unitarity criterion for scattering amplitudes on the noncommutative space-time is considered, as a condition that can be used to shed light on the problem of unitarity violation in noncommutative quantum field theories when time is noncommutative. The unitarity constraints on the partial wave amplitudes in the noncommutative space-time are also derived.
Noncommutative spectral geometry and the deformed Hopf algebra structure of quantum field theory
Mairi Sakellariadou; Antonio Stabile; Giuseppe Vitiello
2013-01-11T23:59:59.000Z
We report the results obtained in the study of Alain Connes noncommutative spectral geometry construction focusing on its essential ingredient of the algebra doubling. We show that such a two-sheeted structure is related with the gauge structure of the theory, its dissipative character and carries in itself the seeds of quantization. From the algebraic point of view, the algebra doubling process has the same structure of the deformed Hops algebra structure which characterizes quantum field theory.
Construction of spin models displaying quantum criticality from quantum field theory
Ivan Glasser; J. Ignacio Cirac; Germán Sierra; Anne E. B. Nielsen
2014-07-23T23:59:59.000Z
We provide a method for constructing finite temperature states of one-dimensional spin chains displaying quantum criticality. These models are constructed using correlators of products of quantum fields and have an analytical purification. Their properties can be investigated by Monte-Carlo simulations, which enable us to study the low-temperature phase diagram and to show that it displays a region of quantum criticality. The mixed states obtained are shown to be close to the thermal state of a simple nearest neighbour Hamiltonian.
Commutativity of Substitution and Variation in Actions of Quantum Field Theory
Zhong Chao Wu
2009-11-11T23:59:59.000Z
There exists a paradox in quantum field theory: substituting a field configuration which solves a subset of the field equations into the action and varying it is not necessarily equivalent to substituting that configuration into the remaining field equations. We take the $S^4$ and Freund-Rubin-like instantons as two examples to clarify the paradox. One must match the specialized configuration field variables with the corresponding boundary conditions by adding appropriate Legendre terms to the action. Some comments are made regarding exceptional degenerate cases.
Milton, K A
2015-01-01T23:59:59.000Z
Starting from the earlier notions of stationary action principles, we show how Julian Schwinger's Quantum Action Principle descended from Dirac's formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. The connection between the two is brought out, and applications are discussed. The Keldysh-Schwinger time-cycle method of extracting matrix elements in nonequilibrium situations is described. The variational formulation of quantum field theory and the development of source theory constitute the latter part of this work. In this document, derived from Schwinger's lectures over four decades, the continuity of concepts, such as that of Green's functions, becomes apparent.
Field Theory and Standard Model
W. Buchmüller; C. Lüdeling
2006-09-18T23:59:59.000Z
This is a short introduction to the Standard Model and the underlying concepts of quantum field theory.
Ultracold Atoms: How Quantum Field Theory Invaded Atomic Physics
Broader source: All U.S. Department of Energy (DOE) Office Webpages (Extended Search)
AFDC Printable Version Share this resource Send a link to EERE: Alternative Fuels Data Center Home Page to someone by E-mail Share EERE: Alternative Fuels Data Center Home Page on Facebook Tweet about EERE: Alternative Fuels Data Center Home Page on Twitter Bookmark EERE: Alternative1 First Use of Energy for All Purposes (Fuel and Nonfuel), 2002; Level:Energy: Grid Integration Redefining What'sis Taking Over OurThe Iron Spin TransitionProgram |Frank CasellaEnergyUltracold Atoms: How Quantum
3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
Winston Fairbairn; Etera R. Livine
2007-02-23T23:59:59.000Z
An effective field theory for matter coupled to three-dimensional quantum gravity was recently derived in the context of spinfoam models in hep-th/0512113. In this paper, we show how this relates to group field theories and generalized matrix models. In the first part, we realize that the effective field theory can be recasted as a matrix model where couplings between matrices of different sizes can occur. In a second part, we provide a family of classical solutions to the three-dimensional group field theory. By studying perturbations around these solutions, we generate the dynamics of the effective field theory. We identify a particular case which leads to the action of hep-th/0512113 for a massive field living in a flat non-commutative space-time. The most general solutions lead to field theories with non-linear redefinitions of the momentum which we propose to interpret as living on curved space-times. We conclude by discussing the possible extension to four-dimensional spinfoam models.
Conserved charges and quantum-group transformations in noncommutative field theories
Giovanni Amelino-Camelia; Giulia Gubitosi; Flavio Mercati; Giacomo Rosati
2010-09-16T23:59:59.000Z
The recently-developed techniques of Noether analysis of the quantum-group spacetime symmetries of some noncommutative field theories rely on the {\\it ad hoc} introduction of some peculiar auxiliary transformation parameters, which appear to have no role in the structure of the quantum group. We here show that it is possible to set up the Noether analysis directly in terms of the quantum-group symmetry transformations, and we therefore establish more robustly the attribution of the conserved charges to the symmetries of interest. We also characterize the concept of "time independence" (as needed for conserved charges) in a way that is robust enough to be applicable even to theories with space/time noncommutativity, where it might have appeared that any characterization of time independence should be vulnerable to changes of ordering convention.
Vladimir Mashkevich
2008-03-13T23:59:59.000Z
The aim of these notes is to elucidate some aspects of quantum field theory in curved spacetime, especially those relating to the notion of particles. A selection of issues relevant to wave-particle duality is given. The case of a generic curved spacetime is outlined. A Hamiltonian formulation of quantum field theory in curved spacetime is elaborated for a preferred reference frame with a separated space metric (a static spacetime and a reductive synchronous reference frame). Applications: (1) Black hole. (2) The universe; the cosmological redshift is obtained in the context of quantum field theory.
Leonardo Mazza; Alejandro Bermudez; Nathan Goldman; Matteo Rizzi; Miguel Angel Martin-Delgado; Maciej Lewenstein
2011-05-04T23:59:59.000Z
We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from non-interacting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize the majority of phases in the periodic table of topological insulators.
Probing Hawking and Unruh effects and quantum field theory in curved space by geometric invariants
Antonio Capolupo; Giuseppe Vitiello
2013-11-12T23:59:59.000Z
The presence of noncyclic geometric invariant is revealed in all the phenomena where particle generation from vacuum or vacuum condensates appear. Aharonov--Anandan invariants then can help to study such systems and can represent a new tool to be used in order to provide laboratory evidence of phenomena particulary hard to be detected, such as Hawking and Unruh effects and some features of quantum field theory in curved space simulated by some graphene morphologies. It is finally suggested that a very precise quantum thermometer can be built by exploiting geometric invariants properties.
Matrix product states and variational methods applied to critical quantum field theory
Ashley Milsted; Jutho Haegeman; Tobias J. Osborne
2014-05-15T23:59:59.000Z
We study the second-order quantum phase-transition of massive real scalar field theory with a quartic interaction ($\\phi^4$ theory) in (1+1) dimensions on an infinite spatial lattice using matrix product states (MPS). We introduce and apply a naive variational conjugate gradient method, based on the time-dependent variational principle (TDVP) for imaginary time, to obtain approximate ground states, using a related ansatz for excitations to calculate the particle and soliton masses and to obtain the spectral density. We also estimate the central charge using finite-entanglement scaling. Our value for the critical parameter agrees well with recent Monte Carlo results, improving on an earlier study which used the related DMRG method, verifying that these techniques are well-suited to studying critical field systems. We also obtain critical exponents that agree, as expected, with those of the transverse Ising model. Additionally, we treat the special case of uniform product states (mean field theory) separately, showing that they may be used to investigate non-critical quantum field theories under certain conditions.
Olivier Coquand; Bruno Machet
2014-07-08T23:59:59.000Z
1-loop quantum corrections are shown to induce large effects on the refraction index n inside a graphene strip in the presence of an external magnetic field B orthogonal to it. To this purpose, we use the tools of Quantum Field Theory to calculate the photon propagator at 1-loop inside graphene in position space, which leads to an effective vacuum polarization in a brane-like theory of photons interacting with massless electrons at locations confined inside the thin strip (its longitudinal spread is considered to be infinite). The effects factorize into quantum ones, controlled by the value of B and that of the electromagnetic coupling alpha, and a "transmittance function" U in which the geometry of the sample and the resulting confinement of electrons play the major roles. We consider photons inside the visible spectrum and magnetic fields in the range 1-20 Teslas. At B=0, quantum effects depend very weakly on alpha and n is essentially controlled by U; we recover, then, an opacity for visible light of the same order of magnitude pi * alpha_{vac} as measured experimentally.
Effective Field Theory for the Quantum Electrodynamics of a Graphene Wire
P. Faccioli; E. Lipparini
2009-06-30T23:59:59.000Z
We study the low-energy quantum electrodynamics of electrons and holes, in a thin graphene wire. We develop an effective field theory (EFT) based on an expansion in p/p_T, where p_T is the typical momentum of electrons and holes in the transverse direction, while p are the momenta in the longitudinal direction. We show that, to the lowest-order in (p/p_T), our EFT theory is formally equivalent to the exactly solvable Schwinger model. By exploiting such an analogy, we find that the ground state of the quantum wire contains a condensate of electron-hole pairs. The excitation spectrum is saturated by electron-hole collective bound-states, and we calculate the dispersion law of such modes. We also compute the DC conductivity per unit length at zero chemical potential and find g_s =e^2/h, where g_s=4 is the degeneracy factor.
Quantum theory Bohrification: topos theory and quantum theory
Spitters, Bas
Quantum theory Bohrification: topos theory and quantum theory Bas Spitters Domains XI, 9/9/2014 Bas Spitters Bohrification: topos theory and quantum theory #12;Quantum theory Point-free Topology The axiom, Krein-Millman, Alaoglu, Hahn-Banach, Gelfand, Zariski, ... Bas Spitters Bohrification: topos theory
The density of states approach for the simulation of finite density quantum field theories
K. Langfeld; B. Lucini; A. Rago; R. Pellegrini; L. Bongiovanni
2015-03-02T23:59:59.000Z
Finite density quantum field theories have evaded first principle Monte-Carlo simulations due to the notorious sign-problem. The partition function of such theories appears as the Fourier transform of the generalised density-of-states, which is the probability distribution of the imaginary part of the action. With the advent of Wang-Landau type simulation techniques and recent advances, the density-of-states can be calculated over many hundreds of orders of magnitude. Current research addresses the question whether the achieved precision is high enough to reliably extract the finite density partition function, which is exponentially suppressed with the volume. In my talk, I review the state-of-play for the high precision calculations of the density-of-states as well as the recent progress for obtaining reliable results from highly oscillating integrals. I will review recent progress for the $Z_3$ quantum field theory for which results can be obtained from the simulation of the dual theory, which appears to free of a sign problem.
Wu, Yue-Liang
2015-01-01T23:59:59.000Z
Treating the gravitational force on the same footing as the electroweak and strong forces, we present a quantum field theory (QFT) of gravity based on spinnic and scaling gauge symmetries. The so-called Gravifield sided on both locally flat non-coordinate space-time and globally flat Minkowski space-time is an essential ingredient for gauging global spinnic and scaling symmetries. The locally flat Gravifield space-time spanned by the Gravifield is associated with a non-commutative geometry characterized by a gauge-type field strength of Gravifield. A gauge invariant and coordinate independent action for the quantum gravity is built in the Gravifield basis, we derive equations of motion for all quantum fields with including the gravitational effect and obtain basic conservation laws for all symmetries. The equation of motion for Gravifield tensor is deduced in connection directly with the energy-momentum tensor. When the spinnic and scaling gauge symmetries are broken down to a background structure that posses...
Cosmological Constant as Vacuum Energy Density of Quantum Field Theories on Noncommutative Spacetime
Xiao-Jun Wang
2004-12-15T23:59:59.000Z
We propose a new approach to understand hierarchy problem for cosmological constant in terms of considering noncommutative nature of space-time. We calculate that vacuum energy density of the noncommutative quantum field theories in nontrivial background, which admits a smaller cosmological constant by introducing an higher noncommutative scale $\\mu_{NC}\\sim M_p$. The result $\\rho_\\Lambda\\sim 10^{-6}\\Lambda_{SUSY}^8M_p^4/\\mu_{NC}^8$ yields cosmological constant at the order of current observed value for supersymmetry breaking scale at 10TeV. It is the same as Banks' phenomenological formula for cosmological constant.
Negative energy densities in integrable quantum field theories at one-particle level
Bostelmann, Henning
2015-01-01T23:59:59.000Z
We study the phenomenon of negative energy densities in quantum field theories with self-interaction. Specifically, we consider a class of integrable models (including the sinh-Gordon model) in which we investigate the expectation value of the energy density in one-particle states. In this situation, we classify the possible form of the stress-energy tensor from first principles. We show that one-particle states with negative energy density generically exist in non-free situations, and we establish lower bounds for the energy density (quantum energy inequalities). Demanding that these inequalities hold reduces the ambiguity in the stress-energy tensor, in some situations fixing it uniquely. Numerical results for the lowest spectral value of the energy density allow us to demonstrate how negative energy densities depend on the coupling constant and on other model parameters.
Negative energy densities in integrable quantum field theories at one-particle level
Henning Bostelmann; Daniela Cadamuro
2015-02-05T23:59:59.000Z
We study the phenomenon of negative energy densities in quantum field theories with self-interaction. Specifically, we consider a class of integrable models (including the sinh-Gordon model) in which we investigate the expectation value of the energy density in one-particle states. In this situation, we classify the possible form of the stress-energy tensor from first principles. We show that one-particle states with negative energy density generically exist in non-free situations, and we establish lower bounds for the energy density (quantum energy inequalities). Demanding that these inequalities hold reduces the ambiguity in the stress-energy tensor, in some situations fixing it uniquely. Numerical results for the lowest spectral value of the energy density allow us to demonstrate how negative energy densities depend on the coupling constant and on other model parameters.
Smooth Field Theories and Homotopy Field Theories
Wilder, Alan Cameron
2011-01-01T23:59:59.000Z
1 . . . . . . . . 4 Categories of Field Theories 4.1 Functorto super symmetric field theories. CRM Proceedings and0-dimensional super symmetric field theories. preprint 2008.
Vukmirovic, Nenad
2010-01-01T23:59:59.000Z
Petersilka, Density Functional Theory (Springer, New York,Quantum Dots: Theory Nenad Vukmirovi´ and Lin-Wang Wang cdensity functional theory; electronic structure; empirical
Introduction to spherical field theory
Dean Lee
1998-11-12T23:59:59.000Z
Spherical field theory is a new non-perturbative method for studying quantum field theories. It uses the spherical partial wave expansion to reduce a general d-dimensional Euclidean field theory into a set of coupled one-dimensional systems. The coupled one-dimensional systems are then converted to partial differential equations and solved numerically. We demonstrate the methods of spherical field theory by analyzing Euclidean phi^4 theory in two dimensions.
A unified quantum theory II: gravity interacting with Yang-Mills and spinor fields
Claus Gerhardt
2014-03-24T23:59:59.000Z
We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces of nature. Using canonical quantization we obtain solutions of the Wheeler-DeWitt equation in a vector bundle and the method of second quantization leads to a symplectic vector space $(V,\\om)$ and a corresponding CCR representation for the bosonic components and a CAR representation for the fermionic part. The solution space of the Wheeler-DeWitt equation is invariant under gauge transformations and under isometries in the spacelike base space $\\so$ of a given Riemannian metric $\\rho_{ij}$. We also define a net of local subalgebras which satisfy four of the Haag-Kastler axioms.
Asymptotic states and renormalization in Lorentz-violating quantum field theory
Mauro Cambiaso; Ralf Lehnert; Robertus Potting
2014-09-09T23:59:59.000Z
Asymptotic single-particle states in quantum field theories with small departures from Lorentz symmetry are investigated perturbatively with focus on potential phenomenological ramifications. To this end, one-loop radiative corrections for a sample Lorentz-violating Lagrangian contained in the Standard-Model Extension (SME) are studied at linear order in Lorentz breakdown. It is found that the spinor kinetic operator, and thus the free-particle physics, is modified by Lorentz-violating operators absent from the original Lagrangian. As a consequence of this result, both the standard renormalization procedure as well as the Lehmann-Symanzik-Zimmermann reduction formalism need to be adapted. The necessary adaptations are worked out explicitly at first order in Lorentz-breaking coefficients.
Mishchenko, Yuriy
2004-12-01T23:59:59.000Z
MISHCHENKO, YURIY. Applications of Canonical Transformations and Nontrivial Vacuum Solutions to flavor mixing and critical phenomena in Quantum Field Theory. (Under the direction of Chueng-Ryong Ji.) In this dissertation we consider two recent applications of Bogoliubov Transformation to the phenomenology of quantum mixing and the theory of critical phenomena. In recent years quantum mixing got in the focus of the searches for New Physics due to its unparalleled sensitivity to SM parameters and indications of neutrino mixing. It was recently suggested that Bogoliubov Transformation may be important in proper definition of the flavor states that otherwise results in problems in perturbative treatment. As first part of this dissertation we investigate this conjecture and develop a complete formulation of such a mixing field theory involving introduction of general formalism, analysis of space-time conversion and phenomenological implications. As second part of this dissertati
CLASSICAL FIELD THEORY WITH Z (3) SYMMETRY
Ruck, H.M.
2010-01-01T23:59:59.000Z
and H.M. Ruck, Quantum field theory Potts model, J. Math.in cyclic symmetry field theories, Nucl. Phys. B167 M.J.waves in nonlinear field theories, Phys. Rev. Lett. 32. R.
A Non-Riemannian Metric on Space-Time Emergent From Scalar Quantum Field Theory
Kar, Arnab
2012-01-01T23:59:59.000Z
We show that the standard deviation \\sigma(x,x') = \\sqrt{} of a scalar quantum field theory is a metric (i.e., a symmetric positive function satisfying the triangle inequality) on space-time (with imaginary time). It is very different from the Euclidean metric |x-x'|: for four dimensional free scalar field theory, \\sigma(x,x') \\to \\frac{\\sigma_{4}}{a^{2}} -\\frac{\\sigma_{4}'}{|x-x'|^{2}} + \\mathrm{O}(|x-x'|^{-3}), as |x-x'|\\to\\infty. According to \\sigma, space-time has a finite diameter \\frac{\\sigma_{4}}{a^{2}} which is not universal (i.e., depends on the UV cut-off a and the regularization method used). The Lipschitz equivalence class of the metric is independent of the cut-off. \\sigma(x,x') is not the length of the geodesic in any Riemannian metric, as it does not have the intermediate point property: for a pair (x,x') there is in general no point x" such that \\sigma(x,x')=\\sigma(x,x")+\\sigma(x",x'). Nevertheless, it is possible to embed space-time in a higher dimensional space of negative curvature so that ...
S. A. Paston; V. A. Franke
1999-01-22T23:59:59.000Z
The relationship between the perturbation theory in light-front coordinates and Lorentz-covariant perturbation theory is investigated. A method for finding the difference between separate terms of the corresponding series without their explicit evaluation is proposed. A procedure of constructing additional counter-terms to the canonical Hamiltonian that compensate this difference at any finite order is proposed. For the Yukawa model, the light-front Hamiltonian with all of these counter-terms is obtained in a closed form. Possible application of this approach to gauge theories is discussed.
Unitarity bounds and RG flows in time dependent quantum field theory
Xi Dong; Bart Horn; Eva Silverstein; Gonzalo Torroba
2012-03-08T23:59:59.000Z
We generalize unitarity bounds on operator dimensions in conformal field theory to field theories with spacetime dependent couplings. Below the energy scale of spacetime variation of the couplings, their evolution can strongly affect the physics, effectively shifting the infrared operator scaling and unitarity bounds determined from correlation functions in the theory. We analyze this explicitly for large-$N$ double-trace flows, and connect these to UV complete field theories. One motivating class of examples comes from our previous work on FRW holography, where this effect explains the range of flavors allowed in the dual, time dependent, field theory.
Unitarity Bounds and RG Flows in Time Dependent Quantum Field Theory
Dong, Xi; Horn, Bart; Silverstein, Eva; Torroba, Gonzalo; /Stanford U., ITP /Stanford U., Phys. Dept. /SLAC
2012-04-05T23:59:59.000Z
We generalize unitarity bounds on operator dimensions in conformal field theory to field theories with spacetime dependent couplings. Below the energy scale of spacetime variation of the couplings, their evolution can strongly affect the physics, effectively shifting the infrared operator scaling and unitarity bounds determined from correlation functions in the theory. We analyze this explicitly for large-N double-trace flows, and connect these to UV complete field theories. One motivating class of examples comes from our previous work on FRW holography, where this effect explains the range of flavors allowed in the dual, time dependent, field theory.
Smooth Field Theories and Homotopy Field Theories
Wilder, Alan Cameron
2011-01-01T23:59:59.000Z
CHAPTER 3. FIELD THEORIES Definition 3.2.1. A smooth fielda ’top down’ definition of field theories. Taking as ourin the following. Definition A field theory is a symmetric
Deformations of Quantum Field Theories and the Construction of Interacting Models
Sabina Alazzawi
2015-03-03T23:59:59.000Z
The subject of this thesis is the rigorous construction of QFT models with nontrivial interaction. Two different approaches in the framework of AQFT are discussed. On the one hand, an inverse scattering problem is considered. A given factorizing S-matrix is thereby taken as the starting point of the construction. The particle spectrum taken into account involves an arbitrary number of massive particle species, transforming under a global gauge group. Starting from known wedge-local auxiliary fields, the transition to local theories is shown. To his end, we make use of the modular nuclearity condition and investigate certain maps from the wedge algebras, generated by the auxiliary fields, to the considered Hilbert space. Under a very plausible conjecture it is shown that these maps are nuclear, which implies the nontriviality of algebras associated with bounded regions in the sense that the Reeh-Schlieder property holds. A large class of integrable models with factorizing S-matrices in 1+1 dimensions can be constructed in this way. Among them are the O(N)-invariant nonlinear sigma-models. Deformation techniques, on the other hand, constitute a method of construction which may be applied in arbitrary spacetime dimensions. This approach starts from a known quantum field theoretic model which is subjected to a certain modification. Here, concretely, the model of a scalar massive Fermion was deformed. The emerging models are based on wedge-local fields, allowing for the computation of the two-particle S-matrix. The resulting scattering matrix depends on the deformation and differs from the one of the initial model. By restricting to 1+1 dimensions, the deformation method yields a large class of integrable models with factorizing S-matrices, including the Sinh-Gordon model.
A Review of Noncommutative Field Theories
Victor O. Rivelles
2011-01-27T23:59:59.000Z
We present a brief review of selected topics in noncommutative field theories ranging from its revival in string theory, its influence on quantum field theories, its possible experimental signatures and ending with some applications in gravity and emergent gravity.
Alfredo Iorio; Gaetano Lambiase
2014-12-15T23:59:59.000Z
The solutions of many issues, of the ongoing efforts to make deformed graphene a tabletop quantum field theory in curved spacetimes, are presented. A detailed explanation of the special features of curved spacetimes, originating from embedding portions of the Lobachevsky plane into $\\mathbf{R}^3$, is given, and the special role of coordinates for the physical realizations in graphene, is explicitly shown, in general, and for various examples. The Rindler spacetime is reobtained, with new important differences with respect to earlier results. The de Sitter spacetime naturally emerges, for the first time, paving the way to future applications in cosmology. The role of the BTZ black hole is also briefly addressed. The singular boundary of the pseudospheres, "Hilbert horizon", is seen to be closely related to event horizon of the Rindler, de Sitter, and BTZ kind. This gives new, and stronger, arguments for the Hawking phenomenon to take place. An important geometric parameter, $c$, overlooked in earlier work, takes here its place for physical applications, and it is shown to be related to graphene's lattice spacing, $\\ell$. It is shown that all surfaces of constant negative curvature, ${\\cal K} = -r^{-2}$, are unified, in the limit $c/r \\to 0$, where they are locally applicable to the Beltrami pseudosphere. This, and $c = \\ell$, allow us a) to have a phenomenological control on the reaching of the horizon; b) to use spacetimes different than Rindler for the Hawking phenomenon; c) to approach the generic surface of the family. An improved expression for the thermal LDOS is obtained. A non-thermal term for the total LDOS is found. It takes into account: a) the peculiarities of the graphene-based Rindler spacetime; b) the finiteness of a laboratory surface; c) the optimal use of the Minkowski quantum vacuum, through the choice of this Minkowski-static boundary.
M. Lapert; R. Tehini; G. Turinici; D. Sugny
2009-05-29T23:59:59.000Z
We consider the optimal control of quantum systems interacting non-linearly with an electromagnetic field. We propose new monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured by a non-standard choice of the cost which is not quadratic in the field. These algorithms can be constructed for pure and mixed-state quantum systems. The efficiency of the method is shown numerically on molecular orientation with a non-linearity of order 3 in the field. Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well-approximated by pulses that could be implemented experimentally.
Robert Carroll
2007-11-05T23:59:59.000Z
We show some relations between Ricci flow and quantum theory via Fisher information and the quantum potential.
Mario G. Silveirinha
2014-06-09T23:59:59.000Z
Here, we develop a comprehensive quantum theory for the phenomenon of quantum friction. Based on a theory of macroscopic quantum electrodynamics for unstable systems, we calculate the quantum expectation of the friction force, and link the friction effect to the emergence of system instabilities related to the Cherenkov effect. These instabilities may occur due to the hybridization of particular guided modes supported by the individual moving bodies, and selection rules for the interacting modes are derived. It is proven that the quantum friction effect can take place even when the interacting bodies are lossless and made of nondispersive dielectrics.
Oshmyansky, A
2007-01-01T23:59:59.000Z
An alternative quantum field theory for gravity is proposed for low energies based on an attractive effect between contaminants in a Bose-Einstein Condensate rather than on particle exchange. In the ``contaminant in condensate effect," contaminants cause a potential in an otherwise uniform condensate, forcing the condensate between two contaminants to a higher energy state. The energy of the system decreases as the contaminants come closer together, causing an attractive force between contaminants. It is proposed that mass-energy may have a similar effect on Einstein's space-time field, and gravity is quantized by the same method by which the contaminant in condensate effect is quantized. The resulting theory is finite and, if a physical condensate is assumed to underly the system, predictive. However, the proposed theory has several flaws at high energies and is thus limited to low energies. Falsifiable predictions are given for the case that the Higgs condensate is assumed to be the condensate underlying gr...
Alexander Oshmyansky
2007-03-08T23:59:59.000Z
An alternative quantum field theory for gravity is proposed for low energies based on an attractive effect between contaminants in a Bose-Einstein Condensate rather than on particle exchange. In the ``contaminant in condensate effect," contaminants cause a potential in an otherwise uniform condensate, forcing the condensate between two contaminants to a higher energy state. The energy of the system decreases as the contaminants come closer together, causing an attractive force between contaminants. It is proposed that mass-energy may have a similar effect on Einstein's space-time field, and gravity is quantized by the same method by which the contaminant in condensate effect is quantized. The resulting theory is finite and, if a physical condensate is assumed to underly the system, predictive. However, the proposed theory has several flaws at high energies and is thus limited to low energies. Falsifiable predictions are given for the case that the Higgs condensate is assumed to be the condensate underlying gravity.
Lucien Hardy
2013-03-06T23:59:59.000Z
We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map between pure states and maximal effects such that we get unit probability. This maximal effect does not give probability equal to one for any other pure state. Information Locality: A maximal measurement is effected on a composite system if we perform maximal measurements on each of the components. Tomographic Locality: The state of a composite system can be determined from the statistics collected by making measurements on the components. Permutability: There exists a reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system. Sturdiness: Filters are non-flattening. To single out quantum theory we need only add any requirement that is inconsistent with classical probability theory and consistent with quantum theory.
Inevitability and Importance of Non-Perturbative Elements in Quantum Field Theory
Alexander P. Bakulev; Dmitry V. Shirkov
2011-02-11T23:59:59.000Z
The subject of the first section-lecture is concerned with the strength and the weakness of the perturbation theory (PT) approach, that is expansion in powers of a small parameter $\\alpha$, in Quantum Theory. We start with outlining a general troublesome feature of the main quantum theory instrument, the perturbation expansion method. The striking issue is that perturbation series in powers of $\\alpha \\ll 1$ is not a convergent series. The formal reason is an essential singularity of quantum amplitude (matrix element) $C(\\alpha)$ at the origin $\\alpha=0$. In many physically important cases one needs some alternative means of theoretical analysis. In particular, this refers to perturbative QCD (pQCD) in the low-energy domain. In the second section-lecture, we discuss the approach of Analytic Perturbation Theory (APT). We start with a short historic preamble and then discuss how combining the Dispersion Relation with the Renormalization Group (RG) techniques yields the APT with \\myMath{\\displaystyle e^{-1/\\alpha}} nonanalyticity. Next we consider the results of APT applications to low-energy QCD processes and show that in this approach the fourth-loop contributions, which appear to be on the asymptotic border in the pQCD approach, are of the order of a few per mil. Then we note that using the RG in QCD dictates the need to use the Fractional APT (FAPT) and describe its basic ingredients. As an example of the FAPT application in QCD we consider the pion form factor $F_\\pi(Q^2)$ calculation. At the end, we discuss the resummation of nonpower series in {(F)APT} with application to the estimation of the Higgs-boson-decay width $\\Gamma_{H\\to\\bar{b}b}(m_H^2)$.
Gauge Theory of Quantum Gravity
J. W. Moffat
1994-01-04T23:59:59.000Z
A gauge theory of quantum gravity is formulated, in which an internal, field dependent metric is introduced which non-linearly realizes the gauge fields on the non-compact group $SL(2,C)$, while linearly realizing them on $SU(2)$. Einstein's $SL(2,C)$ invariant theory of gravity emerges at low energies, since the extra degrees of freedom associated with the quadratic curvature and the internal metric only dominate at high energies. In a fixed internal metric gauge, only the the $SU(2)$ gauge symmetry is satisfied, the particle spectrum is identified and the Hamiltonian is shown to be bounded from below. Although Lorentz invariance is broken in this gauge, it is satisfied in general. The theory is quantized in this fixed, broken symmetry gauge as an $SU(2)$ gauge theory on a lattice with a lattice spacing equal to the Planck length. This produces a unitary and finite theory of quantum gravity.
Matthew James
2014-06-20T23:59:59.000Z
This paper explains some fundamental ideas of {\\em feedback} control of quantum systems through the study of a relatively simple two-level system coupled to optical field channels. The model for this system includes both continuous and impulsive dynamics. Topics covered in this paper include open and closed loop control, impulsive control, optimal control, quantum filtering, quantum feedback networks, and coherent feedback control.
Negative Energies and Field Theory
Gerald E. Marsh
2008-11-20T23:59:59.000Z
The assumption that the vacuum is the minimum energy state, invariant under unitary transformations, is fundamental to quantum field theory. However, the assertion that the conservation of charge implies that the equal time commutator of the charge density and its time derivative vanish for two spatially separated points is inconsistent with the requirement that the vacuum be the lowest energy state. Yet, for quantum field theory to be gauge invariant, this commutator must vanish. This essay explores how this conundrum is resolved in quantum electrodynamics.
Introduction to Renormalization in Field Theory
Ling-Fong Li; Chongqing
2012-08-23T23:59:59.000Z
A simple introduction of renormalization in quantum field theory is discussed. Explanation of concepts is emphasized instead of the technical details.
Noncommutative Cohomological Field Theory and GMS soliton
Tomomi Ishikawa; Shin-Ichiro Kuroki; Akifumi Sako
2001-09-15T23:59:59.000Z
We show that it is possible to construct a quantum field theory that is invariant under the translation of the noncommutative parameter $\\theta_{\\mu\
Tureanu, Anca [High Energy Physics Division, Department of Physical Sciences, University of Helsinki and Helsinki Institute of Physics, P.O. Box 64, FIN-00014 Helsinki (Finland)
2006-09-15T23:59:59.000Z
In the framework of quantum field theory on noncommutative space-time with the symmetry group O(1,1)xSO(2), we prove that the Jost-Lehmann-Dyson representation, based on the causality condition taken in connection with this symmetry, leads to the mere impossibility of drawing any conclusion on the analyticity of the 2{yields}2-scattering amplitude in cos {theta}, {theta} being the scattering angle. Discussions on the possible ways of obtaining high-energy bounds analogous to the Froissart-Martin bound on the total cross section are also presented.
Mathematical quantization of Hamiltonian field theories
A. V. Stoyanovsky
2015-02-04T23:59:59.000Z
We define the renormalized evolution operator of the Schr\\"odinger equation in the infinite dimensional Weyl-Moyal algebra during a time interval for a wide class of Hamiltonians depending on time. This leads to a mathematical definition of quantum field theory $S$-matrix and Green functions. We show that for renormalizable field theories, our theory yields the renormalized perturbation series of perturbative quantum field theory. All the results are based on the Feynman graph series technique.
Polymer Parametrised Field Theory
Alok Laddha; Madhavan Varadarajan
2008-05-02T23:59:59.000Z
Free scalar field theory on 2 dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using LQG type `polymer' representations for the matter field and the inertial variables. The quantum constraints are solved via group averaging techniques and, analogous to the case of spatial geometry in LQG, the smooth (flat) spacetime geometry is replaced by a discrete quantum structure. An overcomplete set of Dirac observables, consisting of (a) (exponentials of) the standard free scalar field creation- annihilation modes and (b) canonical transformations corresponding to conformal isometries, are represented as operators on the physical Hilbert space. None of these constructions suffer from any of the `triangulation' dependent choices which arise in treatments of LQG. In contrast to the standard Fock quantization, the non- Fock nature of the representation ensures that the algebra of conformal isometries as well as that of spacetime diffeomorphisms are represented in an anomaly free manner. Semiclassical states can be analysed at the gauge invariant level. It is shown that `physical weaves' necessarily underly such states and that such states display semiclassicality with respect to, at most, a countable subset of the (uncountably large) set of observables of type (a). The model thus offers a fertile testing ground for proposed definitions of quantum dynamics as well as semiclassical states in LQG.
Diffeomorphism invariant Quantum Field Theories of Connections in terms of webs
Jerzy Lewandowski; Thomas Thiemann
1999-01-07T23:59:59.000Z
In the canonical quantization of gravity in terms of the Ashtekar variables one uses paths in the 3-space to construct the quantum states. Usually, one restricts oneself to families of paths admitting only finite number of isolated intersections. This assumption implies a limitation on the diffeomorphisms invariance of the introduced structures. In this work, using the previous results of Baez and Sawin, we extend the existing results to a theory admitting all the possible piecewise smooth finite paths and loops. In particular, we $(i)$ characterize the spectrum of the Ashtekar-Isham configuration space, $(ii)$ introduce spin-web states, a generalization of the spin-network states, $(iii)$ extend the diffeomorphism averaging to the spin-web states and derive a large class of diffeomorphism invariant states and finally $(iv)$ extend the 3-geometry operators and the Hamiltonian operator.
Three lectures on noncommutative field theories
F. A. Schaposnik
2004-08-18T23:59:59.000Z
Classical and quantum aspects of noncommutative field theories are discussed. In particular, noncommutative solitons and instantons are constructed and also d=2,3 noncommutative fermion and bosonic (Wess-Zumino-Witten and Chern-Simons)theories are analyzed.
Vladimir I. Zverev; Alexander M. Tishin
2009-01-29T23:59:59.000Z
In the given work the first attempt to generalize quantum uncertainty relation on macro objects is made. Business company as one of economical process participants was chosen by the authors for this purpose. The analogies between quantum micro objects and the structures which from the first sight do not have anything in common with physics are given. The proof of generalized uncertainty relation is produced. With the help of generalized uncertainty relation the authors wanted to elaborate a new non-traditional approach to the description of companies' business activity and their developing and try to formulate some advice for them. Thus, our work makes the base of quantum theory of econimics
Renormalisation of Noncommutative Quantum Field Harald Grosse1
Wulkenhaar, Raimar
Renormalisation of Noncommutative Quantum Field Theory Harald Grosse1 and Raimar Wulkenhaar2 1 recall some models for noncommutative space-time and discuss quantum field theories on these deformed. Keywords: noncommutative geometry; quantum field theory; renormalisation AMS Subject Classification: 81T15
Covariant Noncommutative Field Theory
Estrada-Jimenez, S. [Licenciaturas en Fisica y en Matematicas, Facultad de Ingenieria, Universidad Autonoma de Chiapas Calle 4a Ote. Nte. 1428, Tuxtla Gutierrez, Chiapas (Mexico); Garcia-Compean, H. [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN P.O. Box 14-740, 07000 Mexico D.F., Mexico and Centro de Investigacion y de Estudios Avanzados del IPN, Unidad Monterrey Via del Conocimiento 201, Parque de Investigacion e Innovacion Tecnologica (PIIT) Autopista nueva al Aeropuerto km 9.5, Lote 1, Manzana 29, cp. 66600 Apodaca Nuevo Leon (Mexico); Obregon, O. [Instituto de Fisica de la Universidad de Guanajuato P.O. Box E-143, 37150 Leon Gto. (Mexico); Ramirez, C. [Facultad de Ciencias Fisico Matematicas, Universidad Autonoma de Puebla, P.O. Box 1364, 72000 Puebla (Mexico)
2008-07-02T23:59:59.000Z
The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.
High energy cosmic rays experiments inspired by noncommutative quantum field theory
Josip Trampetic
2012-10-19T23:59:59.000Z
Phenomenological analysis of the covariant theta-exact noncommutative (NC) gauge field theory (GFT), inspired by high energy cosmic rays experiments, is performed in the framework of the inelastic neutrino-nucleon scatterings, plasmon and $Z$-boson decays into neutrino pair, the Big Bang Nucleosynthesis (BBN) and the Reheating Phase After Inflation (RPAI), respectively. Next we have have found neutrino two-point function and shows a closed form decoupling of the hard ultraviolet (UV) divergent term from softened ultraviolet/infrared (UV/IR) mixing term and from the finite terms as well. For a certain choice of the noncommutative parameter theta which preserves unitarity, problematic UV divergent and UV/IR mixing terms vanish. Non-perturbative modifications of the neutrino dispersion relations are assymptotically independent of the scale of noncommutativity in both the low and high energy limits and may allow superluminal propagation.
Josip Trampetic
2013-02-04T23:59:59.000Z
Analysis of the covariant theta-exact noncommutative (NC) gauge field theory (GFT), inspired by high energy cosmic rays experiments, is performed in the framework of the inelastic neutrino-nucleon scatterings. Next we have have found neutrino two-point function and shows a closed form decoupled from the hard ultraviolet (UV) divergent term, from softened ultraviolet/infrared (UV/IR) mixing term, and from the finite terms as well. For a certain choice of the noncommutative parameter theta which preserves unitarity, problematic UV divergent and UV/IR mixing terms vanish. Non-perturbative modifications of the neutrino dispersion relations are assymptotically independent of the scale of noncommutativity in both, the low and high energy limits and may allow superluminal propagation.
Quantum fields with classical perturbations
Derezi?ski, Jan, E-mail: Jan.Derezinski@fuw.edu.pl [Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Hoza 74, 00-682 Warszawa (Poland)
2014-07-15T23:59:59.000Z
The main purpose of these notes is a review of various models of Quantum Field Theory (QFT) involving quadratic Lagrangians. We discuss scalar and vector bosons, spin 1/2 fermions, both neutral and charged. Beside free theories, we study their interactions with classical perturbations, called, depending on the context, an external linear source, mass-like term, current or electromagnetic potential. The notes may serve as a first introduction to QFT.
Quantum communication, reference frames and gauge theory
S. J. van Enk
2006-04-26T23:59:59.000Z
We consider quantum communication in the case that the communicating parties not only do not share a reference frame but use imperfect quantum communication channels, in that each channel applies some fixed but unknown unitary rotation to each qubit. We discuss similarities and differences between reference frames within that quantum communication model and gauge fields in gauge theory. We generalize the concept of refbits and analyze various quantum communication protocols within the communication model.
Particle decay in Ising field theory with magnetic field
Gesualdo Delfino
2007-03-30T23:59:59.000Z
The scaling limit of the two-dimensional Ising model in the plane of temperature and magnetic field defines a field theory which provides the simplest illustration of non-trivial phenomena such as spontaneous symmetry breaking and confinement. Here we discuss how Ising field theory also gives the simplest model for particle decay. The decay widths computed in this theory provide the obvious test ground for the numerical methods designed to study unstable particles in quantum field theories discretized on a lattice.
Kirrander, Adam [Laboratoire Aime Cotton du CNRS, Universite de Paris-Sud, Batiment 505, F-91405 Orsay (France); Shalashilin, Dmitrii V. [School of Chemistry, University of Leeds, Leeds LS2 9JT (United Kingdom)
2011-09-15T23:59:59.000Z
We present an alternate version of the coupled-coherent-state method, specifically adapted for solving the time-dependent Schroedinger equation for multielectron dynamics in atoms and molecules. This theory takes explicit account of the exchange symmetry of fermion particles, and it uses fermion molecular dynamics to propagate trajectories. As a demonstration, calculations in the He atom are performed using the full Hamiltonian and accurate experimental parameters. Single- and double-ionization yields by 160-fs and 780-nm laser pulses are calculated as a function of field intensity in the range 10{sup 14}-10{sup 16} W/cm{sup 2}, and good agreement with experiments by Walker et al. is obtained. Since this method is trajectory based, mechanistic analysis of the dynamics is straightforward. We also calculate semiclassical momentum distributions for double ionization following 25-fs and 795-nm pulses at 1.5x10{sup 15} W/cm{sup 2}, in order to compare them with the detailed experiments by Rudenko et al. For this more challenging task, full convergence is not achieved. However, major effects such as the fingerlike structures in the momentum distribution are reproduced.
A note on ${\\cal N}\\ge 6$ Superconformal Quantum Field Theories in three dimensions
Denis Bashkirov
2011-08-20T23:59:59.000Z
Based on the structure of the three-dimensional superconformal algebra we show that every irreducible ${\\mathcal N}=6$ three-dimensional superconformal theory containes exactly one conserved U(1)-symmetry current in the stress tensor supermultiplet and that superconformal symmetry of every ${\\mathcal N}=7$ superconformal theory is in fact enhanced to ${\\mathcal N}=8$. Moreover, an irreducible ${\\cal N}=8$ superconformal theory does not have any global symmetries. The first observation explains why all known examples of ${\\mathcal N}=6$ superconformal theories have a global abelian symmetry.
Noncommutative field theory from twisted Fock space
Bu, Jong-Geon; Kim, Hyeong-Chan; Lee, Youngone; Vac, Chang Hyon; Yee, Jae Hyung [Department of Physics, Yonsei University, Seoul (Korea, Republic of)
2006-06-15T23:59:59.000Z
We construct a quantum field theory in noncommutative space time by twisting the algebra of quantum operators (especially, creation and annihilation operators) of the corresponding quantum field theory in commutative space time. The twisted Fock space and S-matrix consistent with this algebra have been constructed. The resultant S-matrix is consistent with that of Filk [Tomas Filk, Phys. Lett. B 376, 53 (1996).]. We find from this formulation that the spin-statistics relation is not violated in the canonical noncommutative field theories.
C. S. Lam
1994-06-24T23:59:59.000Z
A low energy string theory should reduce to an ordinary quantum field theory, but in reality the structures of the two are so different as to make the equivalence obscure. The string formalism is more symmetrical between the spacetime and the internal degrees of freedom, thus resulting in considerable simplification in practical calculations and novel insights in theoretical understandings. We review here how tree or multiloop field-theoretical diagrams can be organized in a string-like manner to take advantage of this computational and conceptual simplicity.
Hull, Chris
The zero modes of closed strings on a torus — the torus coordinates plus dual coordinates conjugate to winding number — parameterize a doubled torus. In closed string field theory, the string field depends on all zero-modes ...
Quantum field theory in the presence of a medium: Green's function expansions
Kheirandish, Fardin [Department of Physics, Islamic Azad University, Shahreza-Branch, Shahreza (Iran, Islamic Republic of); Salimi, Shahriar [Department of Physics, University of Kurdistan, Sanandaj (Iran, Islamic Republic of)
2011-12-15T23:59:59.000Z
Starting from a Lagrangian and using functional-integration techniques, series expansions of Green's function of a real scalar field and electromagnetic field, in the presence of a medium, are obtained. The parameter of expansion in these series is the susceptibility function of the medium. Relativistic and nonrelativistic Langevin-type equations are derived. Series expansions for Lifshitz energy in finite temperature and for an arbitrary matter distribution are derived. Covariant formulations for both scalar and electromagnetic fields are introduced. Two illustrative examples are given.
Diffeomorphisms in group field theories
Baratin, Aristide [Triangle de la Physique, CPHT Ecole Polytechnique, IPhT Saclay, LPT Orsay and Laboratoire de Physique Theorique, CNRS UMR 8627, Universite Paris XI, F-91405 Orsay Cedex (France); Girelli, Florian [School of Physics, University of Sydney, Sydney, New South Wales 2006 (Australia); Oriti, Daniele [Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Muehlenberg 1, 14467 Golm (Germany)
2011-05-15T23:59:59.000Z
We study the issue of diffeomorphism symmetry in group field theories (GFT), using the noncommutative metric representation introduced by A. Baratin and D. Oriti [Phys. Rev. Lett. 105, 221302 (2010).]. In the colored Boulatov model for 3d gravity, we identify a field (quantum) symmetry which ties together the vertex translation invariance of discrete gravity, the flatness constraint of canonical quantum gravity, and the topological (coarse-graining) identities for the 6j symbols. We also show how, for the GFT graphs dual to manifolds, the invariance of the Feynman amplitudes encodes the discrete residual action of diffeomorphisms in simplicial gravity path integrals. We extend the results to GFT models for higher-dimensional BF theories and discuss various insights that they provide on the GFT formalism itself.
Noncommutative Dipole Field Theories
K. Dasgupta; M. M. Sheikh-Jabbari
2002-02-05T23:59:59.000Z
Assigning an intrinsic constant dipole moment to any field, we present a new kind of associative star product, the dipole star product, which was first introduced in [hep-th/0008030]. We develop the mathematics necessary to study the corresponding noncommutative dipole field theories. These theories are sensible non-local field theories with no IR/UV mixing. In addition we discuss that the Lorentz symmetry in these theories is ``softly'' broken and in some particular cases the CP (and even CPT) violation in these theories may become observable. We show that a non-trivial dipole extension of N=4, D=4 gauge theories can only be obtained if we break the SU(4) R (and hence super)-symmetry. Such noncommutative dipole extensions, which in the maximal supersymmetric cases are N=2 gauge theories with matter, can be embedded in string theory as the theories on D3-branes probing a smooth Taub-NUT space with three form fluxes turned on or alternatively by probing a space with R-symmetry twists. We show the equivalences between the two approaches and also discuss the M-theory realization.
Three approaches to classical thermal field theory
Gozzi, E., E-mail: gozzi@ts.infn.it [Department of Physics, University of Trieste, Strada Costiera 11, Miramare - Grignano, 34151 Trieste (Italy); INFN, Sezione di Trieste (Italy); Penco, R., E-mail: rpenco@syr.edu [Department of Physics, Syracuse University, Syracuse, NY 13244-1130 (United States)
2011-04-15T23:59:59.000Z
Research Highlights: > Classical thermal field theory admits three equivalent path integral formulations. > Classical Feynman rules can be derived for all three formulations. > Quantum Feynman rules reduce to classical ones at high temperatures. > Classical Feynman rules become much simpler when superfields are introduced. - Abstract: In this paper we study three different functional approaches to classical thermal field theory, which turn out to be the classical counterparts of three well-known different formulations of quantum thermal field theory: the closed-time path (CTP) formalism, the thermofield dynamics (TFD) and the Matsubara approach.
Variational methods for field theories
Ben-Menahem, S.
1986-09-01T23:59:59.000Z
Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.
viii Contents. Three Field Theory. 87—89. 90—95. 96—97. 98—107. 108—114. 115—121. De?nition and examples of ?eld structure 67. Vector spaces, bases ...
A Kinetic Theory Approach to Quantum Gravity
B. L. Hu
2002-04-22T23:59:59.000Z
We describe a kinetic theory approach to quantum gravity -- by which we mean a theory of the microscopic structure of spacetime, not a theory obtained by quantizing general relativity. A figurative conception of this program is like building a ladder with two knotted poles: quantum matter field on the right and spacetime on the left. Each rung connecting the corresponding knots represent a distinct level of structure. The lowest rung is hydrodynamics and general relativity; the next rung is semiclassical gravity, with the expectation value of quantum fields acting as source in the semiclassical Einstein equation. We recall how ideas from the statistical mechanics of interacting quantum fields helped us identify the existence of noise in the matter field and its effect on metric fluctuations, leading to the establishment of the third rung: stochastic gravity, described by the Einstein-Langevin equation. Our pathway from stochastic to quantum gravity is via the correlation hierarchy of noise and induced metric fluctuations. Three essential tasks beckon: 1) Deduce the correlations of metric fluctuations from correlation noise in the matter field; 2) Reconstituting quantum coherence -- this is the reverse of decoherence -- from these correlation functions 3) Use the Boltzmann-Langevin equations to identify distinct collective variables depicting recognizable metastable structures in the kinetic and hydrodynamic regimes of quantum matter fields and how they demand of their corresponding spacetime counterparts. This will give us a hierarchy of generalized stochastic equations -- call them the Boltzmann-Einstein hierarchy of quantum gravity -- for each level of spacetime structure, from the macroscopic (general relativity) through the mesoscopic (stochastic gravity) to the microscopic (quantum gravity).
Covariant Hamiltonian Field Theory
Jürgen Struckmeier; Andreas Redelbach
2012-05-22T23:59:59.000Z
A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation theory offers more general means for defining mappings that preserve the form of the field equations than the usual Lagrangian description. It is proved that Poisson brackets, Lagrange brackets, and canonical 2-forms exist that are invariant under canonical transformations of the fields. The technique to derive transformation rules for the fields from generating functions is demonstrated by means of various examples. In particular, it is shown that the infinitesimal canonical transformation furnishes the most general form of Noether's theorem. We furthermore specify the generating function of an infinitesimal space-time step that conforms to the field equations.
STATISTICAL MECHANICS AND FIELD THEORY
Samuel, S.A.
2010-01-01T23:59:59.000Z
York. K. Bardakci, Field Theory for Solitons, II, BerkeleyFart I Applications of Field Theory Methods to StatisticalStatistical Mechanics to Field Theory Chapter IV The Grand
Theory of electromagnetic fields
Wolski, Andrzej
2011-01-01T23:59:59.000Z
We discuss the theory of electromagnetic fields, with an emphasis on aspects relevant to radiofrequency systems in particle accelerators. We begin by reviewing Maxwell's equations and their physical significance. We show that in free space, there are solutions to Maxwell's equations representing the propagation of electromagnetic fields as waves. We introduce electromagnetic potentials, and show how they can be used to simplify the calculation of the fields in the presence of sources. We derive Poynting's theorem, which leads to expressions for the energy density and energy flux in an electromagnetic field. We discuss the properties of electromagnetic waves in cavities, waveguides and transmission lines.
Encoding field theories into gravities
Aoki, Sinya; Onogi, Tetsuya
2015-01-01T23:59:59.000Z
We propose a method, which encodes the information of a $d$ dimensional quantum field theory into a $d+1$ dimensional gravity in the $1/N$ expansion. We first construct a $d+1$ dimensional field theory from the $d$ dimensional one via the gradient flow equation, whose flow time $t$ represents the energy scale of the system such that $t\\rightarrow 0$ corresponds to the ultra-violet (UV) while $t\\rightarrow\\infty$ to the infra-red (IR). We then define the induced metric from $d+1$ dimensional field operators. We show that the metric defined in this way becomes classical in the large $N$ limit, in a sense that quantum fluctuations of the metric are suppressed as $1/N$ due to the large $N$ factorization property. As a concrete example, we apply our method to the O(N) non-linear $\\sigma$ model in two dimensions. We calculate the induced metric in three dimensions, which is shown to describe De Sitter (dS) or Anti De Sitter (AdS) space in the massless limit, where the mass is dynamically generated in the O(N) non-l...
Effective Hamiltonian Constraint from Group Field Theory
Etera R. Livine; Daniele Oriti; James P. Ryan
2011-04-28T23:59:59.000Z
Spinfoam models provide a covariant formulation of the dynamics of loop quantum gravity. They are non-perturbatively defined in the group field theory (GFT) framework: the GFT partition function defines the sum of spinfoam transition amplitudes over all possible (discretized) geometries and topologies. The issue remains, however, of explicitly relating the specific form of the group field theory action and the canonical Hamiltonian constraint. Here, we suggest an avenue for addressing this issue. Our strategy is to expand group field theories around non-trivial classical solutions and to interpret the induced quadratic kinematical term as defining a Hamiltonian constraint on the group field and thus on spin network wave functions. We apply our procedure to Boulatov group field theory for 3d Riemannian gravity. Finally, we discuss the relevance of understanding the spectrum of this Hamiltonian operator for the renormalization of group field theories.
Quantum Theory: a Pragmatist Approach
Richard Healey
2010-08-23T23:59:59.000Z
While its applications have made quantum theory arguably the most successful theory in physics, its interpretation continues to be the subject of lively debate within the community of physicists and philosophers concerned with conceptual foundations. This situation poses a problem for a pragmatist for whom meaning derives from use. While disputes about how to use quantum theory have arisen from time to time, they have typically been quickly resolved, and consensus reached, within the relevant scientific sub-community. Yet rival accounts of the meaning of quantum theory continue to proliferate . In this article I offer a diagnosis of this situation and outline a pragmatist solution to the problem it poses, leaving further details for subsequent articles.
Noncommutative Quantization for Noncommutative Field Theory
Yasumi Abe
2006-07-06T23:59:59.000Z
We present a new procedure for quantizing field theory models on a noncommutative spacetime. The new quantization depends on the noncommutative parameter explicitly and reduces to the canonical quantization in the commutative limit. It is shown that a quantum field theory constructed by the new quantization yeilds exactly the same correlation functions as those of the commutative field theory, that is, the noncommutative effects disappear completely after quantization. This implies, for instance, that by using the new quantization, the noncommutativity can be incorporated in the process of quantization, rahter than in the action as conventionally done.
Nikolai N. Bogolubov, Jr.; Anatoliy K. Prykarpatsky
2008-10-21T23:59:59.000Z
The main fundamental principles characterizing the vacuum field structure are formulated and the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The work is devoted to studying the vacuum structure, special relativity, electrodynamics of interacting charged point particles and quantum mechanics, and is a continuation of \\cite{BPT,BRT1}. Based on the vacuum field theory no-geometry approach, the Lagrangian and Hamiltonian reformulation of some alternative classical electrodynamics models is devised. The Dirac type quantization procedure, based on the canonical Hamiltonian formulation, is developed for some alternative electrodynamics models. Within an approach developed a possibility of the combined description both of electrodynamics and gravity is analyzed.
Non-commutative Field Theory with Twistor-like Coordinates
Tomasz R. Taylor
2007-09-16T23:59:59.000Z
We consider quantum field theory in four-dimensional Minkowski spacetime, with the position coordinates represented by twistors instead of the usual world-vectors. Upon imposing canonical commutation relations between twistors and dual twistors, quantum theory of fields described by non-holomorphic functions of twistor variables becomes manifestly non-commutative, with Lorentz symmetry broken by a time-like vector. We discuss the free field propagation and its impact on the short- and long-distance behavior of physical amplitudes in perturbation theory. In the ultraviolet limit, quantum field theories in twistor space are generically less divergent than their commutative counterparts. Furthermore, there is no infrared--ultraviolet mixing problem.
The vacuum state functional of interacting string field theory
A. Ilderton
2005-06-21T23:59:59.000Z
We show that the vacuum state functional for both open and closed string field theories can be constructed from the vacuum expectation values it must generate. The method also applies to quantum field theory and as an application we give a diagrammatic description of the equivalance between Schrodinger and covariant repreresentations of field theory.
Quantum theory of tensionless noncommutative p-branes
Gamboa, J. [Departamento de Fisica, Universidad de Santiago de Chile, Casilla 307, Santiago 2 (Chile); Loewe, M. [Facultad de Fisica, Pontificia Universidad Catolica de Chile, Casilla 306, Santiago 22 (Chile); Mendez, F. [INFN, Laboratorio Nazionali del Gran Sasso, SS, 17bis, 67010 Asergi, L'Aquila (Italy)
2004-11-15T23:59:59.000Z
The quantum theory involving noncommutative tensionless p-branes is studied following path integral methods. Our procedure allows a simple treatment for generally covariant noncommutative extended systems and it contains, as a particular case, the thermodynamics and the quantum tensionless string theory. The effect induced by noncommutativity in the field space is to produce a confinement among pairing of null p-branes.
Gerold Doyen; Deiana Drakova
2014-08-12T23:59:59.000Z
We construct a world model consisting of a matter field living in 4 dimensional spacetime and a gravitational field living in 11 dimensional spacetime. The seven hidden dimensions are compactified within a radius estimated by reproducing the particle - wave characteristic of diffraction experiments. In the presence of matter fields the gravitational field develops localized modes with elementary excitations called gravonons which are induced by the sources (massive particles). The final world model treated here contains only gravonons and a scalar matter field. The solution of the Schroedinger equation for the world model yields matter fields which are localized in the 4 dimensional subspace. The localization has the following properties: (i) There is a chooser mechanism for the selection of the localization site. (ii) The chooser selects one site on the basis of minor energy differences and differences in the gravonon structure between the sites, which appear statistical. (iii) The changes from one localization site to a neighbouring one take place in a telegraph-signal like manner. (iv) The times at which telegraph like jumps occur dependent on subtleties of the gravonon structure which appear statistical. (v) The fact that the dynamical law acts in the configuration space of fields living in 11 dimensional spacetime lets the events observed in 4 dimensional spacetime appear non-local. In this way the phenomenology of Copenhagen quantum mechanics is obtained without the need of introducing the process of collapse and a probabilistic interpretation of the wave function. Operators defining observables need not be introduced. All experimental findings are explained in a deterministic way as a consequence of the time development of the wave function in configuration space according to Schroedinger's equation.
Effective Field Theory for Bound State Reflection
Michelle Pine; Dean Lee
2013-01-17T23:59:59.000Z
Elastic quantum bound-state reflection from a hard-wall boundary provides direct information regarding the structure and compressibility of quantum bound states. We discuss elastic quantum bound-state reflection and derive a general theory for elastic reflection of shallow dimers from hard-wall surfaces using effective field theory. We show that there is a small expansion parameter for analytic calculations of the reflection scattering length. We present a calculation up to second order in the effective Hamiltonian in one, two, and three dimensions. We also provide numerical lattice results for all three cases as a comparison with our effective field theory results. Finally, we provide an analysis of the compressibility of the alpha particle confined to a cubic lattice with vanishing Dirichlet boundaries.
Transgression field theory for interacting topological insulators
Aç?k, Özgür
2013-01-01T23:59:59.000Z
We consider effective topological field theories of quantum Hall systems and time-reversal invariant topological insulators that are Chern-Simons and BF field theories. The edge states of these systems are related to the gauge invariance of the effective actions. For the edge states at the interface of two topological insulators, transgression field theory is proposed as a gauge invariant effective action. Transgression actions of Chern-Simons theories for (2+1)D and (4+1)D and BF theories for (3+1)D are constructed. By using transgression actions, the edge states are written in terms of the bulk connections of effective Chern-Simons and BF theories.
Unified Field Theories Hitoshi Murayama
Murayama, Hitoshi
Unified Field Theories Hitoshi Murayama Department of Physics, University of California Berkeley This article explains the idea of unified field theories in particle physics. It starts with a historical review of two successful theories which unified two apparently distinct forces: Maxwell's theory
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Reformulating and Reconstructing Quantum Theory
Lucien Hardy
2011-08-25T23:59:59.000Z
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. The mathematical axioms for quantum theory are the following: [Axiom 1] Operations correspond to operators. [Axiom 2] Every complete set of physical operators corresponds to a complete set of operations. The following operational postulates are shown to be equivalent to these mathematical axioms: [P1] Sharpness. Associated with any given pure state is a unique maximal effect giving probability equal to one. This maximal effect does not give probability equal to one for any other pure state. [P2] Information locality. A maximal measurement on a composite system is effected if we perform maximal measurements on each of the components. [P3] Tomographic locality. The state of a composite system can be determined from the statistics collected by making measurements on the components. [P4] Compound permutability. There exists a compound reversible transformation on any system effecting any given permutation of any given maximal set of distinguishable states for that system. [P5] Sturdiness. Filters are non-flattening. Hence, from these postulates we can reconstruct all the usual features of quantum theory: States are represented by positive operators, transformations by completely positive trace non-increasing maps, and effects by positive operators. The Born rule (i.e. the trace rule) for calculating probabilitieso follows. A more detailed abstract is provided in the paper.
Quantum Mechanics and Representation Theory Columbia University
Woit, Peter
Quantum Mechanics and Representation Theory Peter Woit Columbia University Texas Tech, November 21 2013 Peter Woit (Columbia University) Quantum Mechanics and Representation Theory November 2013 1 / 30, 1967 Peter Woit (Columbia University) Quantum Mechanics and Representation Theory November 2013 2 / 30
Low-Energy Effective Theories of Quantum Link and Quantum Spin Models
B. Schlittgen; U. -J. Wiese
2000-12-11T23:59:59.000Z
Quantum spin and quantum link models provide an unconventional regularization of field theory in which classical fields arise via dimensional reduction of discrete variables. This D-theory regularization leads to the same continuum theories as the conventional approach. We show this by deriving the low-energy effective Lagrangians of D-theory models using coherent state path integral techniques. We illustrate our method for the $(2+1)$-d Heisenberg quantum spin model which is the D-theory regularization of the 2-d O(3) model. Similarly, we prove that in the continuum limit a $(2+1)$-d quantum spin model with $SU(N)_L\\times SU(N)_R\\times U(1)_{L=R}$ symmetry is equivalent to the 2-d principal chiral model. Finally, we show that $(4+1)$-d SU(N) quantum link models reduce to ordinary 4-d Yang-Mills theory.
Dmitriy Palatnik
2005-08-12T23:59:59.000Z
Suggested modification of the Einstein-Maxwell system, such that Maxwell equations become non-gauge and nonlinear. The theory is based on assumption that observable (i.e., felt by particles) metric is $ {\\tilde{g}}_{ab} = g_{ab} - l^2{A}_a{A}_b$, where $g_{ab}$ is metric (found from Einstein equations), $A_a$ is electromagnetic potential, and $l$ is fundamental constant of the theory. Specific model of the mass and charge densities of a fundamental particle is considered. As a result, one obtains solutions corresponding to quantized electrical charge with spectrum $q_{n} = {{2n}\\over3}e$ and $q'_{n} = -{(2n+1)\\over3}e$, where $n = 0, 1, 2, ...$ Theory predicts Coulomb interaction between electrical charges and masses. Namely, if ($m, e$) and ($m',e'$) describe masses and electrical charges of two particles respectively, then energy of interaction (in non-relativistic limit) is $V(r) = [ee' - kmm' - \\sqrt k(em' + e'm)]/r$. It follows, then, that the Earth's mass, $M_E$, contributes negative electrical charge, $Q_E = - \\sqrt k M_E$, which explains why primary cosmic rays consist mainly of positively charged particles. One may attribute the fairweather electric field at the Earth's surface to the charge $Q_E$.
Remote State Preparation for Quantum Fields
Ran Ber; Erez Zohar
2015-01-07T23:59:59.000Z
Remote state preparation is generation of a desired state by a remote observer. In spite of causality, it is well known, according to the Reeh-Schlieder theorem, that it is possible for relativistic quantum field theories, and a "physical" process achieving this task, involving superoscillatory functions, has recently been introduced. In this work we deal with non-relativistic fields, and show that remote state preparation is also possible for them, hence generalizing the Reeh-Schlieder theorem.
Two quantum effects in the theory of gravitation
Robinson, Sean Patrick, 1977-
2005-01-01T23:59:59.000Z
We will discuss two methods by which the formalism of quantum field theory can be included in calculating the physical effects of gravitation. In the first of these, the consequences of treating general relativity as an ...
Diagrammar in classical scalar field theory
Cattaruzza, E., E-mail: Enrico.Cattaruzza@gmail.com [Department of Physics (Miramare Campus), University of Trieste, Strada Costiera 11, Miramare-Grignano 34014, Trieste (Italy); Gozzi, E., E-mail: gozzi@ts.infn.it [Department of Physics (Miramare Campus), University of Trieste, Strada Costiera 11, Miramare-Grignano 34014, Trieste (Italy); INFN, Sezione di Trieste (Italy); Francisco Neto, A., E-mail: antfrannet@gmail.com [Departamento de Engenharia de Producao, Administracao e Economia, Escola de Minas, Campus Morro do Cruzeiro, UFOP, 35400-000 Ouro Preto MG (Brazil)
2011-09-15T23:59:59.000Z
In this paper we analyze perturbatively a g{phi}{sup 4}classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplify the calculations and make the classical perturbative calculations almost 'identical' formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem. - Highlights: > We provide the Feynman diagrams of perturbation theory for a classical field theory. > We give a super-formalism which links the quantum diagrams to the classical ones. > We check perturbatively the fluctuation-dissipation theorem.
Noncommutative Quantum Scalar Field Cosmology
Diaz Barron, L. R.; Lopez-Dominguez, J. C.; Sabido, M. [Departamento de Fisica, DCI-Campus Leon, Universidad de Guanajuato, A.P. E-143, C.P. 37150, Guanajuato (Mexico); Yee, C. [Departamento de Matematicas, Facultad de Ciencias, Universidad Autonoma de Baja California, Ensenada, Baja California (Mexico)
2010-07-12T23:59:59.000Z
In this work we study noncommutative Friedmann-Robertson-Walker (FRW) cosmology coupled to a scalar field endowed with an exponential potential. The quantum scenario is analyzed in the Bohmian formalism of quantum trajectories to investigate the effects of noncommutativity in the evolution of the universe.
Exterior Differential Systems for Field Theories
Frank B. Estabrook
2015-02-24T23:59:59.000Z
Exterior Differential Systems (EDS) and Cartan forms, set in the state space of field variables taken together with four space-time variables, are formulated for classical gauge theories of Maxwell and SU(2) Yang-Mills fields minimally coupled to Dirac spinor multiplets. Cartan character tables are calculated, showing whether the EDS, and so the Euler-Lagrange partial differential equations, is well-posed. The first theory, with 22 dimensional state space (10 Maxwell field and potential components and 8 components of a Dirac field), anticipates QED. In the second, non-Abelian, case (30 Yang-Mills field components and 16 Dirac), only if three additional "ghost" fields are included (15 more scalar variables) is a well-posed EDS found. This classical formulation anticipates the need for introduction of Fadeev-Popov ghost fields in the quantum standard model.
A Noncommutative Deformation of Topological Field Theory
Hugo Garcia-Compean; Pablo Paniagua
2004-02-21T23:59:59.000Z
Cohomological Yang-Mills theory is formulated on a noncommutative differentiable four manifold through the $\\theta$-deformation of its corresponding BRST algebra. The resulting noncommutative field theory is a natural setting to define the $\\theta$-deformation of Donaldson invariants and they are interpreted as a mapping between the Chevalley-Eilenberg homology of noncommutative spacetime and the Chevalley-Eilenberg cohomology of noncommutative moduli of instantons. In the process we find that in the weak coupling limit the quantum theory is localized at the moduli space of noncommutative instantons.
Quantum theory and the role of mind in nature
Henry P. Stapp
2001-03-09T23:59:59.000Z
Orthodox Copenhagen quantum theory renounces the quest to understand the reality in which we are imbedded, and settles for practical rules describing connections between our observations. Many physicist have regarded this renunciation of our effort to describe nature herself as premature, and John von Neumann reformulated quantum theory as a theory of an evolving objective universe interacting with human consciousness. This interaction is associated both in Copenhagen quantum theory and in von Neumann quantum theory with a sudden change that brings the objective physical state of a system in line with a subjectively felt psychical reality. The objective physical state is thereby converted from a material substrate to an informational and dispositional substrate that carries both the information incorporated into it by the psychical realities, and certain dispositions for the occurrence of future psychical realities. The present work examines and proposes solutions to two problems that have appeared to block the development of this conception of nature. The first problem is how to reconcile this theory with the principles of relativistic quantum field theory; the second problem is to understand whether, strictly within quantum theory, a person's mind can affect the activities of his brain, and if so how. Solving the first problem involves resolving a certain nonlocality question. The proposed solution to the second problem is based on a postulated connection between effort, attention, and the quantum Zeno effect. This solution explains on the basis of quantum physics a large amount of heretofore unexplained data amassed by psychologists.
Gauge Theory of Gravity Requires Massive Torsion Field
Rainer W. Kuhne
1998-06-04T23:59:59.000Z
One of the greatest unsolved issues of the physics of this century is to find a quantum field theory of gravity. According to a vast amount of literature unification of quantum field theory and gravitation requires a gauge theory of gravity which includes torsion and an associated spin field. Various models including either massive or massless torsion fields have been suggested. We present arguments for a massive torsion field, where the probable rest mass of the corresponding spin three gauge boson is the Planck mass.
Quantum theory of gravitational collapse (lecture notes on quantum conchology)
Petr Hajicek
2002-04-15T23:59:59.000Z
Preliminary version No.~2 of the lecture notes for the talk ``Quantum theory of gravitational collapse'' given at the 271. WE-Heraeus-Seminar ``Aspects of Quantum Gravity'' at Bad Honnef, 25 February--1 March 2002
Vector field theories in cosmology
A. Tartaglia; N. Radicella
2007-08-05T23:59:59.000Z
Recently proposed theories based on the cosmic presence of a vectorial field are compared and contrasted. In particular the so called Einstein aether theory is discussed in parallel with a recent proposal of a strained space-time theory (Cosmic Defect theory). We show that the latter fits reasonably well the cosmic observed data with only one, or at most two, adjustable parameters, whilst other vector theories use much more. The Newtonian limits are also compared. Finally we show that the CD theory may be considered as a special case of the aether theories, corresponding to a more compact and consistent paradigm.
D-brane effective field theory from string field theory
Washington Taylor
2000-02-15T23:59:59.000Z
Open string field theory is considered as a tool for deriving the effective action for the massless or tachyonic fields living on D-branes. Some simple calculations are performed in open bosonic string field theory which validate this approach. The level truncation method is used to calculate successive approximations to the quartic terms \\phi^4, (A^\\mu A_\\mu)^2 and [A_\\mu, A_\
PCT Theorem in Field Theory on Noncommutative Space
Namit Mahajan
2003-07-29T23:59:59.000Z
The PCT theorem is shown to be valid in quantum field theory formulated on noncommutative spacetime by exploiting the properties of the Wightman functions defined in such a set up.
Nonequilibrium field theory from the 2PI effective action
Szabolcs Borsanyi
2005-12-22T23:59:59.000Z
Nonperturbative approximation schemes are inevitable even in weakly coupled theories if the nonequilibrium behavior of quantum fields is investigated. The two-particle irreducible (2PI) effective action formalism provides an efficient framework for obtaining resummation schemes both in and out of equilibrium. We briefly review the these techniques and discuss recent findings for nonequilibrium field theories.
Infinitely many inequivalent field theories from one Lagrangian
Carl M. Bender; Daniel W. Hook; Nick E. Mavromatos; Sarben Sarkar
2014-08-11T23:59:59.000Z
Logarithmic time-like Liouville quantum field theory has a generalized PT invariance, where T is the time-reversal operator and P stands for an S-duality reflection of the Liouville field $\\phi$. In Euclidean space the Lagrangian of such a theory, $L=\\frac{1}{2}(\
Hiroaki Matsueda
2014-08-27T23:59:59.000Z
An information-geometrical interpretation of AdS3/CFT2 correspondence is given. In particular, we consider an inverse problem in which the classical spacetime metric is given in advance and then we find what is the proper quantum information that is well stored into the spacetime. We see that the Fisher metric plays a central role on this problem. Actually, if we start with the two-dimensional hyperbolic space, a constant-time surface in AdS3, the resulting singular value spectrum of the quantum state shows power law for the correlation length with conformal dimension proportional to the curvature radius in the gravity side. Furthermore, the entanglement entropy data embedded into the hyperbolic space agree well with the Ryu-Takayanagi formula. These results show that the relevance of the AdS/CFT correspondence can be represented by the information-gemetrical approach based on the Fisher metric.
Noncommutative Field Theories and Gravity
Victor O. Rivelles
2003-02-21T23:59:59.000Z
We show that after the Seiberg-Witten map is performed the action for noncommutative field theories can be regarded as a coupling to a field dependent gravitational background. This gravitational background depends only on the gauge field. Charged and uncharged fields couple to different backgrounds and we find that uncharged fields couple more strongly than the charged ones. We also show that the background is that of a gravitational plane wave. A massless particle in this background has a velocity which differs from the velocity of light and we find that the deviation is larger in the uncharged case. This shows that noncommutative field theories can be seen as ordinary theories in a gravitational background produced by the gauge field with a charge dependent gravitational coupling.
Quantum control theory and applications: A survey
Daoyi Dong; Ian R Petersen
2011-01-10T23:59:59.000Z
This paper presents a survey on quantum control theory and applications from a control systems perspective. Some of the basic concepts and main developments (including open-loop control and closed-loop control) in quantum control theory are reviewed. In the area of open-loop quantum control, the paper surveys the notion of controllability for quantum systems and presents several control design strategies including optimal control, Lyapunov-based methodologies, variable structure control and quantum incoherent control. In the area of closed-loop quantum control, the paper reviews closed-loop learning control and several important issues related to quantum feedback control including quantum filtering, feedback stabilization, LQG control and robust quantum control.
H. Kleinert
2012-10-09T23:59:59.000Z
While free and weakly interacting particles are well described by a a second-quantized nonlinear Schr\\"odinger field, or relativistic versions of it, the fields of strongly interacting particles are governed by effective actions, whose quadratic terms are extremized by fractional wave equations. Their particle orbits perform universal L\\'evy walks rather than Gaussian random walks with perturbations.
Field Theory Techniques on Spin Systems Physics 230A, Spring 2007, Hitoshi Murayama
Murayama, Hitoshi
Field Theory Techniques on Spin Systems Physics 230A, Spring 2007, Hitoshi Murayama 1 Introduction to understand using the quantum field theory techniques. In order to use techniques in continuum field theory would like to do now is to rewrite this Hamiltonian in terms of continuum field theory. The first step
Kwak, Seung Ki
2012-01-01T23:59:59.000Z
The existence of momentum and winding modes of closed string on a torus leads to a natural idea that the field theoretical approach of string theory should involve winding type coordinates as well as the usual space-time ...
Scalar Field Theory on Supermanifolds
Mir Hameeda
2012-05-21T23:59:59.000Z
In this paper we will analyse a scalar field theory on a spacetime with noncommutative and non-anticommutative coordinates. This will be done using supermanifold formalism. We will also analyse its quantization in path integral formalism.
Double field theory at order ??
Hohm, Olaf
We investigate ?? corrections of bosonic strings in the framework of double field theory. The previously introduced “doubled ??-geometry” gives ??-deformed gauge transformations arising in the Green-Schwarz anomaly ...
On Quantum Computation Theory Wim van Dam
ten Cate, Balder
On Quantum Computation Theory Wim van Dam #12;#12;On Quantum Computation Theory #12;ILLC woensdag 9 oktober 2002, te 14.00 uur door Willem Klaas van Dam geboren te Breda. #12;Promotor: Prof. dr. P Dam, 2002 ISBN: 9057760916 #12;" . . . Many errors have been made in the world which today
Pastore, S. [University of South Carolina; Wiringa, Robert B. [ANL; Pieper, Steven C. [ANL; Schiavilla, Rocco [Old Dominion U., JLAB
2014-08-01T23:59:59.000Z
We report quantum Monte Carlo calculations of electromagnetic transitions in $^8$Be. The realistic Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon potentials are used to generate the ground state and nine excited states, with energies that are in excellent agreement with experiment. A dozen $M1$ and eight $E2$ transition matrix elements between these states are then evaluated. The $E2$ matrix elements are computed only in impulse approximation, with those transitions from broad resonant states requiring special treatment. The $M1$ matrix elements include two-body meson-exchange currents derived from chiral effective field theory, which typically contribute 20--30\\% of the total expectation value. Many of the transitions are between isospin-mixed states; the calculations are performed for isospin-pure states and then combined with the empirical mixing coefficients to compare to experiment. In general, we find that transitions between states that have the same dominant spatial symmetry are in decent agreement with experiment, but those transitions between different spatial symmetries are often significantly underpredicted.
Whiteheadian process and quantum theory
Stapp, H.
1998-08-01T23:59:59.000Z
There are deep similarities between Whitehead's idea of the process by which nature unfolds and the ideas of quantum theory. Whitehead says that the world is made of ''actual occasions'', each of which arises from potentialities created by prior actual occasions. These actual occasions are happenings modeled on experiential events, each of which comes into being and then perishes, only to be replaced by a successor. It is these experience-like happenings that are the basic realities of nature, according to Whitehead, not the persisting physical particles that Newtonian physics took be the basic entities. Similarly, Heisenberg says that what is really happening in a quantum process is the emergence of an actual from potentialities created by prior actualities. In the orthodox Copenhagen interpretation of quantum theory the actual things to which the theory refer are increments in ''our knowledge''. These increments are experiential events. The particles of classical physics lose their fundamental status: they dissolve into diffuse clouds of possibilities. At each stage of the unfolding of nature the complete cloud of possibilities acts like the potentiality for the occurrence of a next increment in knowledge, whose occurrence can radically change the cloud of possibilities/potentialities for the still-later increments in knowledge. The fundamental difference between these ideas about nature and the classical ideas that reigned from the time of Newton until this century concerns the status of the experiential aspects of nature. These are things such as thoughts, ideas, feelings, and sensations. They are distinguished from the physical aspects of nature, which are described in terms of quantities explicitly located in tiny regions of space and time. According to the ideas of classical physics the physical world is made up exclusively of things of this latter type, and the unfolding of the physical world is determined by causal connections involving only these things. Thus experiential-type things could be considered to influence the flow of physical events only insofar as they themselves were completely determined by physical things. In other words, experiential-type qualities. insofar as they could affect the flow of physical events, could--within the framework of classical physics--not be free: they must be completely determined by the physical aspects of nature that are, by themselves,sufficient to determine the flow of physical events.
Metric perturbation theory of quantum dynamics
Antony L Tambyrajah
2006-10-06T23:59:59.000Z
A theory of quantum dynamics based on a discrete structure underlying the space time manifold is developed for single particles. It is shown that at the micro domain the interaction of particles with the underlying discrete structure results in the quantum space time manifold. Regarding the resulting quantum space-time as perturbation from the Lorentz metric it is shown it is possible to discuss the dynamics of particles in the quantum domain.
David J. Gross; Washington Taylor
2001-06-27T23:59:59.000Z
We describe the ghost sector of cubic string field theory in terms of degrees of freedom on the two halves of a split string. In particular, we represent a class of pure ghost BRST operators as operators on the space of half-string functionals. These BRST operators were postulated by Rastelli, Sen, and Zwiebach to give a description of cubic string field theory in the closed string vacuum arising from condensation of a D25-brane in the original tachyonic theory. We find a class of solutions for the ghost equations of motion using the pure ghost BRST operators. We find a vanishing action for these solutions, and discuss possible interpretations of this result. The form of the solutions we find in the pure ghost theory suggests an analogous class of solutions in the original theory on the D25-brane with BRST operator Q_B coupling the matter and ghost sectors.
Field Theory on Curved Noncommutative Spacetimes
Alexander Schenkel; Christoph F. Uhlemann
2010-08-03T23:59:59.000Z
We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative spacetimes by using (Abelian) Drinfel'd twists and the associated *-products and *-differential geometry. In particular, we allow for position dependent noncommutativity and do not restrict ourselves to the Moyal-Weyl deformation. We construct action functionals for real scalar fields on noncommutative curved spacetimes, and derive the corresponding deformed wave equations. We provide explicit examples of deformed Klein-Gordon operators for noncommutative Minkowski, de Sitter, Schwarzschild and Randall-Sundrum spacetimes, which solve the noncommutative Einstein equations. We study the construction of deformed Green's functions and provide a diagrammatic approach for their perturbative calculation. The leading noncommutative corrections to the Green's functions for our examples are derived.
Quantum measure and integration theory
Stan Gudder
2009-09-11T23:59:59.000Z
This article begins with a review of quantum measure spaces. Quantum forms and indefinite inner-product spaces are then discussed. The main part of the paper introduces a quantum integral and derives some of its properties. The quantum integral's form for simple functions is characterized and it is shown that the quantum integral generalizes the Lebesgue integral. A bounded, monotone convergence theorem for quantum integrals is obtained and it is shown that a Radon-Nikodym type theorem does not hold for quantum measures. As an example, a quantum-Lebesgue integral on the real line is considered.
Quantum mechanical effects from deformation theory
Much, A. [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)] [Max-Planck-Institute for Mathematics in the Sciences, 04103 Leipzig, Germany and Institute for Theoretical Physics, University of Leipzig, 04009 Leipzig (Germany)
2014-02-15T23:59:59.000Z
We consider deformations of quantum mechanical operators by using the novel construction tool of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a role. Furthermore, a quantum plane can be defined by using the deformation techniques. This in turn gives an experimentally verifiable effect.
Failure of microcausality in noncommutative field theories
Soloviev, M. A. [P. N. Lebedev Physical Institute, Russian Academy of Sciences, Leninsky Prospect 53, Moscow 119991 (Russian Federation)
2008-06-15T23:59:59.000Z
We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking O(x)=:{phi}*{phi}:(x) as a sample observable. Using methods of the theory of distributions, we precisely describe the support properties of the commutator [O(x),O(y)] and prove that, in the case of space-space noncommutativity, it does not vanish at spacelike separation in the noncommuting directions. However, the matrix elements of this commutator exhibit a rapid falloff along an arbitrary spacelike direction irrespective of the type of noncommutativity. We also consider the star commutator for this observable and show that it fails to vanish even at spacelike separation in the commuting directions and completely violates causality. We conclude with a brief discussion about the modified Wightman functions which are vacuum expectation values of the star products of fields at different spacetime points.
Failure of microcausality in noncommutative field theories
Michael A. Soloviev
2008-06-26T23:59:59.000Z
We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking $O(x)=:\\phi\\star\\phi:(x)$ as a sample observable. Using methods of the theory of distributions, we precisely describe the support properties of the commutator [O(x),O(y)] and prove that, in the case of space-space noncommutativity, it does not vanish at spacelike separation in the noncommuting directions. However, the matrix elements of this commutator exhibit a rapid falloff along an arbitrary spacelike direction irrespective of the type of noncommutativity. We also consider the star commutator for this observable and show that it fails to vanish even at spacelike separation in the commuting directions and completely violates causality. We conclude with a brief discussion about the modified Wightman functions which are vacuum expectation values of the star products of fields at different spacetime points.
David J. Gross; Washington Taylor
2001-06-04T23:59:59.000Z
We describe projection operators in the matter sector of Witten's cubic string field theory using modes on the right and left halves of the string. These projection operators represent a step towards an analytic solution of the equations of motion of the full string field theory, and can be used to construct Dp-brane solutions of the string field theory when the BRST operator Q is taken to be pure ghost, as suggested in the recent conjecture by Rastelli, Sen and Zwiebach. We show that a family of solutions related to the sliver state are rank one projection operators on the appropriate space of half-string functionals, and we construct higher rank projection operators corresponding to configurations of multiple D-branes.
CONFORMAL INVARIANT QUANTUM FIELD THEORY CONFORMAL INVARIANT QUANTUM FIELD THEORY
Boyer, Edmond
according to \\r( There and below the dotted lines in the bubble may serve to remind one that the amplitude, in which an n-point Green function will be represented by a bubble with n long legs. The dressed 2-point function (propagator) will be represented by a line and sawing off a leg from a bubble means amputation
Phenomenology of Noncommutative Field Theories
Christopher D. Carone
2004-09-29T23:59:59.000Z
Experimental limits on the violation of four-dimensional Lorentz invariance imply that noncommutativity among ordinary spacetime dimensions must be small. In this talk, I review the most stringent bounds on noncommutative field theories and suggest a possible means of evading them: noncommutativity may be restricted to extra, compactified spatial dimensions. Such theories have a number of interesting features, including Abelian gauge fields whose Kaluza-Klein excitations have self couplings. We consider six-dimensional QED in a noncommutative bulk, and discuss the collider signatures of the model.
Topos theory and `neo-realist' quantum theory
Andreas Doering
2007-12-24T23:59:59.000Z
Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves as a `mathematical universe' with an internal logic, which is used to assign truth-values to all propositions about a physical system. We show in detail how this works for (algebraic) quantum theory.
Inflation and deformation of conformal field theory
Garriga, Jaume; Urakawa, Yuko, E-mail: jaume.garriga@ub.edu, E-mail: yurakawa@ffn.ub.es [Departament de Física Fonamental i Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona (Spain)
2013-07-01T23:59:59.000Z
It has recently been suggested that a strongly coupled phase of inflation may be described holographically in terms of a weakly coupled quantum field theory (QFT). Here, we explore the possibility that the wave function of an inflationary universe may be given by the partition function of a boundary QFT. We consider the case when the field theory is a small deformation of a conformal field theory (CFT), by the addition of a relevant operator O, and calculate the primordial spectrum predicted in the corresponding holographic inflation scenario. Using the Ward-Takahashi identity associated with Weyl rescalings, we derive a simple relation between correlators of the curvature perturbation ? and correlators of the deformation operator O at the boundary. This is done without specifying the bulk theory of gravitation, so that the result would also apply to cases where the bulk dynamics is strongly coupled. We comment on the validity of the Suyama-Yamaguchi inequality, relating the bi-spectrum and tri-spectrum of the curvature perturbation.
Quantum feedback control and classical control theory
Doherty, Andrew C. [Department of Physics, University of Auckland, Private Bag 92019, Auckland, (New Zealand)] [Department of Physics, University of Auckland, Private Bag 92019, Auckland, (New Zealand); Habib, Salman [Theoretical Division, T-8, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)] [Theoretical Division, T-8, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Jacobs, Kurt [Theoretical Division, T-8, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)] [Theoretical Division, T-8, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Mabuchi, Hideo [Norman Bridge Laboratory of Physics 12-33, California Institute of Technology, Pasadena, California 91125 (United States)] [Norman Bridge Laboratory of Physics 12-33, California Institute of Technology, Pasadena, California 91125 (United States); Tan, Sze M. [Department of Physics, University of Auckland, Private Bag 92019, Auckland, (New Zealand)] [Department of Physics, University of Auckland, Private Bag 92019, Auckland, (New Zealand)
2000-07-01T23:59:59.000Z
We introduce and discuss the problem of quantum feedback control in the context of established formulations of classical control theory, examining conceptual analogies and essential differences. We describe the application of state-observer-based control laws, familiar in classical control theory, to quantum systems and apply our methods to the particular case of switching the state of a particle in a double-well potential. (c) 2000 The American Physical Society.
Propagators for Noncommutative Field Theories
R. Gurau; V. Rivasseau; F. Vignes-Tourneret
2006-02-06T23:59:59.000Z
In this paper we provide exact expressions for propagators of noncommutative Bosonic or Fermionic field theories after adding terms of the Grosse-Wulkenhaar type in order to ensure Langmann-Szabo covariance. We emphasize the new Fermionic case and we give in particular all necessary bounds for the multiscale analysis and renormalization of the noncommutative Gross-Neveu model.
Topics in quantum field theory
Kibble, T. W. B.
1958-01-01T23:59:59.000Z
The subject matter of this thesis falls into two distinct parts. Chapters II to IV are devoted to a discussion of Schwinger's action principle, and chapters V and VI are concerned with the proof of dispersion relations ...
Comments on Cahill's Quantum Foam Inflow Theory of Gravity
T. D. Martin
2004-07-20T23:59:59.000Z
We reveal an underlying flaw in Reginald T. Cahill's recently promoted quantum foam inflow theory of gravity. It appears to arise from a confusion of the idea of the Galilean invariance of the acceleration of an individual flow with what is obtained as an acceleration when a homogeneous flow is superposed with an inhomogeneous flow. We also point out that the General Relativistic covering theory he creates by substituting a generalized Painleve-Gullstrand metric into Einstein's field equations leads to absurd results.
Hamilton-Jacobi Theory in k-Symplectic Field Theories
M. De LeÓn; D. MartÍn De Diego; J. C. Marrero; M. Salgado; S. Vilariño
2010-05-10T23:59:59.000Z
In this paper we extend the geometric formalism of Hamilton-Jacobi theory for Mechanics to the case of classical field theories in the k-symplectic framework.
Spin-Statistics and CPT Theorems in Noncommutative Field Theory
M. Chaichian; K. Nishijima; A. Tureanu
2002-09-01T23:59:59.000Z
We show that Pauli's spin-statistics relation remains valid in noncommutative quantum field theories (NC QFT), with the exception of some peculiar cases of noncommutativity between space and time. We also prove that, while the individual symmetries C and T, and in some cases also P, are broken, the CPT theorem still holds in general for noncommutative field theories, in spite of the inherent nonlocality and violation of Lorentz invariance.
Quantum theory from one global symmetry
Chris Fields
2014-06-17T23:59:59.000Z
It is shown that unitary quantum theory is not only consistent with but follows from decompositional equivalence: the principle that there is no preferred decomposition of the universe into systems, or alternatively, that there is no preferred quantum reference frame. Decompositional equivalence requires unitary quantum theory to be both observer- and scale-independent, requires time, "systems" and all classical information to be strictly observer-relative, and imposes an unavoidable free-energy cost on the acquisition of observational outcomes. This free energy cost of observation is characterized from first principles and shown to accord with known costs of information acquisition and storage by human observers.
Conformal field theories with infinitely many conservation laws
Todorov, Ivan [Institut des Hautes Etudes Scientifiques F-91440, Bures-sur-Yvette (France)] [Institut des Hautes Etudes Scientifiques F-91440, Bures-sur-Yvette (France)
2013-02-15T23:59:59.000Z
Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of dimension D-2 they were demonstrated to be generated by bilocal normal products of free massless scalar fields with an O(N), U(N), or Sp(2N) (global) gauge symmetry [B. Bakalov, N. M. Nikolov, K.-H. Rehren, and I. Todorov, 'Unitary positive energy representations of scalar bilocal fields,' Commun. Math. Phys. 271, 223-246 (2007); e-print arXiv:math-ph/0604069v3; and 'Infinite dimensional Lie algebras in 4D conformal quantum field theory,' J. Phys. A Math Theor. 41, 194002 (2008); e-print arXiv:0711.0627v2 [hep-th
Remarks on Time-Space Noncommutative Field Theories
L. Alvarez-Gaume; J. L. F. Barbon; R. Zwicky
2001-03-09T23:59:59.000Z
We propose a physical interpretation of the perturbative breakdown of unitarity in time-like noncommutative field theories in terms of production of tachyonic particles. These particles may be viewed as a remnant of a continuous spectrum of undecoupled closed-string modes. In this way, we give a unified view of the string-theoretical and the field-theoretical no-go arguments against time-like noncommutative theories. We also perform a quantitative study of various locality and causality properties of noncommutative field theories at the quantum level.
Supersymmetry and Gravity in Noncommutative Field Theories
Victor O. Rivelles
2003-05-14T23:59:59.000Z
We discuss the renormalization properties of noncommutative supersymmetric theories. We also discuss how the gauge field plays a role similar to gravity in noncommutative theories.
Yangian Superalgebras in Conformal Field Theory
Thomas Creutzig
2010-12-07T23:59:59.000Z
Quantum Yangian symmetry in several sigma models with supergroup or supercoset as target is established. Starting with a two-dimensional conformal field theory that has current symmetry of a Lie superalgebra with vanishing Killing form we construct non-local charges and compute their properties. Yangian axioms are satisfied, except that the Serre relations only hold for a subsector of the space of fields. Yangian symmetry implies that correlation functions of fields in this sector satisfy Ward identities. We then show that this symmetry is preserved by certain perturbations of the conformal field theory. The main example are sigma models of the supergroups PSL(N|N), OSP(2N+2|2N) and D(2,1;\\alpha) away from the WZW point. Further there are the OSP(2N+2|2N) Gross-Neveu models and current-current perturbations of ghost systems, both for the disc as world-sheet. The latter we show to be equivalent to CP^{N-1|N} sigma models, while the former are conjecturally dual to supersphere sigma models.
Entropy of Quantum Fields in de Sitter Space-time
M. V. Takook
2014-08-15T23:59:59.000Z
The quantum states or Hilbert spaces for the quantum field theory in de Sitter space-time are studied on ambient space formalism. In this formalism, the quantum states are only depended $(1)$ on the topological character of the de Sitter space-time, {\\it i.e.} $\\R \\times S^3$, and $(2)$ on the homogeneous spaces which are used for construction of the unitary irreducible representation of de Sitter group. A compact homogeneous space is chosen in this paper. The unique feature of this homogeneous space is that its total number of quantum states, ${\\cal N}$, is finite although the Hilbert space has infinite dimensions. It is shown that ${\\cal N}$ is a continuous function of the Hubble constant $H$ and the eigenvalue of the Casimir operators of de Sitter group. The entropy of the quantum fields on this Hilbert space have been calculated which is finite and invariant for all inertial observers on the de Sitter hyperboloid.
Quantum Signatures of Spacetime Graininess Quantum Signatures of Spacetime
Quantum Field Theory on Noncommutative Spacetime Implementing Poincaré Symmetry Hopf Algebras, Drinfel Quantum Mechanics on Noncommutative Spacetime 4 Quantum Field Theory on Noncommutative Spacetime Covariant Derivatives and Field Strength Noncommutative Gauge Theories 6 Signatures of Spin
Formalism Locality in Quantum Theory and Quantum Gravity
Lucien Hardy
2008-04-01T23:59:59.000Z
We expect a theory of Quantum Gravity to be both probabilistic and have indefinite causal structure. Indefinite causal structure poses particular problems for theory formulation since many of the core ideas used in the usual approaches to theory construction depend on having definite causal structure. For example, the notion of a state across space evolving in time requires that we have some definite causal structure so we can define a state on a space-like hypersurface. We will see that many of these problems are mitigated if we are able to formulate the theory in a "formalism local" (or F-local) fashion. A formulation of a physical theory is said to be F-local if, in making predictions for any given arbitrary space-time region, we need only refer to mathematical objects pertaining to that region. This is a desirable property both on the grounds of efficiency and since, if we have indefinite causal structure, it is not clear how to select some other space-time region on which our calculations may depend. The usual ways of formulating physical theories (the time evolving state picture, the histories approach, and the local equations approach) are not F-local. We set up a framework for probabilistic theories with indefinite causal structure. This, the causaloid framework, is F-local. We describe how Quantum Theory can be formulated in the causaloid framework (in an F-local fashion). This provides yet another formulation of Quantum Theory. This formulation, however, may be particularly relevant to the problem of finding a theory of Quantum Gravity.
The trouble with orbits: the Stark effect in the old and the new quantum theory
Anthony Duncan; Michel Janssen
2014-04-21T23:59:59.000Z
The old quantum theory and Schr\\"odinger's wave mechanics (and other forms of quantum mechanics) give the same results for the line splittings in the first-order Stark effect in hydrogen, the leading terms in the splitting of the spectral lines emitted by a hydrogen atom in an external electric field. We examine the account of the effect in the old quantum theory, which was hailed as a major success of that theory, from the point of view of wave mechanics. First, we show how the new quantum mechanics solves a fundamental problem one runs into in the old quantum theory with the Stark effect. It turns out that, even without an external field, it depends on the coordinates in which the quantum conditions are imposed which electron orbits are allowed in a hydrogen atom. The allowed energy levels and hence the line splittings are independent of the coordinates used but the size and eccentricity of the orbits are not. In the new quantum theory, this worrisome non-uniqueness of orbits turns into the perfectly innocuous non-uniqueness of bases in Hilbert space. Second, we review how the so-called WKB (Wentzel-Kramers-Brillouin) approximation method for solving the Schr\\"odinger equation reproduces the quantum conditions of the old quantum theory amended by some additional half-integer terms. These extra terms remove the need for some arbitrary extra restrictions on the allowed orbits that the old quantum theory required over and above the basic quantum conditions
Finite field-dependent symmetries in perturbative quantum gravity
Upadhyay, Sudhaker, E-mail: sudhaker@boson.bose.res.in
2014-01-15T23:59:59.000Z
In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation. -- Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and anti-BRST transformations are developed in linear and non-linear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and non-linear gauges is established. •Using BV formulation the results are established at quantum level also.
Generalized Probability Theories: What determines the structure of quantum theory?
Peter Janotta; Haye Hinrichsen
2014-08-13T23:59:59.000Z
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical structure of quantum theory. This review paper tries to present the framework and recent results to a broader readership in an accessible manner. To achieve this, we follow a constructive approach. Starting from few basic physically motivated assumptions we show how a given set of observations can be manifested in an operational theory. Furthermore, we characterize consistency conditions limiting the range of possible extensions. In this framework classical and quantum theory appear as special cases, and the aim is to understand what distinguishes quantum mechanics as the fundamental theory realized in nature. It turns out non-classical features of single systems can equivalently result from higher dimensional classical theories that have been restricted. Entanglement and non-locality, however, are shown to be genuine non-classical features.
On strategy of relativistic quantum theory construction
Yuri A. Rylov
2006-01-16T23:59:59.000Z
Two different strategies of the relativistic quantum theory construction are considered and evaluated. The first strategy is the conventional strategy, based on application of the quantum mechanics technique to relativistic systems. This approach cannot solve the problem of pair production. The apparent success of QFT at solution of this problem is conditioned by the inconsistency of QFT, when the commutation relations are incompatible with the dynamic equations. (The inconsistent theory "can solve" practically any problem, including the problem of pair production). The second strategy is based on application of fundamental principles of classical dynamics and those of statistical description to relativistic dynamic systems. It seems to be more reliable, because this strategy does not use quantum principles, and the main problem of QFT (join of nonrelativistic quantum principles with the principles of relativity) appears to be eliminated.
Topics in low-dimensional field theory
Crescimanno, M.J.
1991-04-30T23:59:59.000Z
Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density.
Topological Field Theory of Time-Reversal Invariant Insulators
Xiao-Liang Qi; Taylor Hughes; Shou-Cheng Zhang
2008-02-24T23:59:59.000Z
We show that the fundamental time reversal invariant (TRI) insulator exists in 4+1 dimensions, where the effective field theory is described by the 4+1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2+1 dimensions. The TRI quantum spin Hall insulator in 2+1 dimensions and the topological insulator in 3+1 dimension can be obtained as descendants from the fundamental TRI insulator in 4+1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the $Z_2$ topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant $\\alpha=e^2/\\hbar c$. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.
Topological Field Theory of Time-Reversal Invariant Insulators
Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19T23:59:59.000Z
We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.
Risk, ambiguity and quantum decision theory
Riccardo Franco
2007-11-06T23:59:59.000Z
In the present article we use the quantum formalism to describe the effects of risk and ambiguity in decision theory. The main idea is that the probabilities in the classic theory of expected utility are estimated probabilities, and thus do not follow the classic laws of probability theory. In particular, we show that it is possible to use consistently the classic expected utility formula, where the probability associated to the events are computed with the equation of quantum interference. Thus we show that the correct utility of a lottery can be simply computed by adding to the classic expected utility a new corrective term, the uncertainty utility, directly connected with the quantum interference term.
Lattice p-Form Electromagnetism and Chain Field Theory
Derek K. Wise
2005-10-08T23:59:59.000Z
Since Wilson's work on lattice gauge theory in the 1970s, discrete versions of field theories have played a vital role in fundamental physics. But there is recent interest in certain higher dimensional analogues of gauge theory, such as p-form electromagnetism, including the Kalb-Ramond field in string theory, and its nonabelian generalizations. It is desirable to discretize such `higher gauge theories' in a way analogous to lattice gauge theory, but with the fundamental geometric structures in the discretization boosted in dimension. As a step toward studying discrete versions of more general higher gauge theories, we consider the case of p-form electromagnetism. We show that discrete p-form electromagnetism admits a simple algebraic description in terms of chain complexes of abelian groups. Moreover, the model allows discrete spacetimes with quite general geometry, in contrast to the regular cubical lattices usually associated with lattice gauge theory. After constructing a suitable model of discrete spacetime for p-form electromagnetism, we quantize the theory using the Euclidean path integral formalism. The main result is a description of p-form electromagnetism as a `chain field theory' -- a theory analogous to topological quantum field theory, but with chain complexes replacing manifolds. This, in particular, gives a notion of time evolution from one `spacelike slice' of discrete spacetime to another.
Minimal coupling method and the dissipative scalar field theory
Fardin Kheirandish; Majid Amooshahi
2005-07-20T23:59:59.000Z
Quantum field theory of a damped vibrating string as the simplest dissipative scalar field investigated by its coupling with an infinit number of Klein-Gordon fields as the environment by introducing a minimal coupling method. Heisenberg equation containing a dissipative term proportional to velocity obtained for a special choice of coupling function and quantum dynamics for such a dissipative system investigated. Some kinematical relations calculated by tracing out the environment degrees of freedom. The rate of energy flowing between the system and it's environment obtained.
From operator algebras to superconformal field theory
Kawahigashi, Yasuyuki [Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153-8914 (Japan)
2010-01-15T23:59:59.000Z
We survey operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory of Jones, and certain aspects of noncommutative geometry of Connes.
Coulomb interactions within Halo Effective Field Theory
Renato Higa
2007-11-30T23:59:59.000Z
I present preliminary results of effective field theory applied to nuclear cluster systems, where Coulomb interactions play a significant role.
Translational Invariance and Noncommutative Field Theories
Orfeu Bertolami
2004-02-02T23:59:59.000Z
Implications of noncommutative field theories with commutator of the coordinates of the form $[x^{\\mu},x^{\
Reasonable fermionic quantum information theories require relativity
Nicolai Friis
2015-02-16T23:59:59.000Z
We show that any abstract quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity. While quantum information may be encoded in the Fock space generated by such operators, the unrestricted fermionic theory has a peculiar feature: Pairs of bipartition marginals of pure states need not have identical spectra. This leads to an ambiguous definition of the entropy of entanglement. We prove that this problem is removed by a superselection rule that arises from Lorentz invariance and no-signalling.
Quantum Electric Field Fluctuations and Potential Scattering
Huang, Haiyun
2015-01-01T23:59:59.000Z
Some physical effects of time averaged quantum electric field fluctuations are discussed. The one loop radiative correction to potential scattering are approximately derived from simple arguments which invoke vacuum electric field fluctuations. For both above barrier scattering and quantum tunneling, this effect increases the transmission probability. It is argued that the shape of the potential determines a sampling function for the time averaging of the quantum electric field operator. We also suggest that there is a nonperturbative enhancement of the transmission probability which can be inferred from the probability distribution for time averaged electric field fluctuations.
Bootstrapping Fuzzy Scalar Field Theory
Christian Saemann
2015-04-13T23:59:59.000Z
We describe a new way of rewriting the partition function of scalar field theory on fuzzy complex projective spaces as a solvable multitrace matrix model. This model is given as a perturbative high-temperature expansion. At each order, we present an explicit analytic expression for most of the arising terms; the remaining terms are computed explicitly up to fourth order. The method presented here can be applied to any model of hermitian matrices. Our results confirm constraints previously derived for the multitrace matrix model by Polychronakos. A further implicit expectation about the shape of the multitrace terms is however shown not to be true.
Noncommutative effective theory of vortices in a complex scalar field
C. D. Fosco; A. Lopez
2002-03-08T23:59:59.000Z
We derive a noncommutative theory description for vortex configurations in a complex field in 2+1 dimensions. We interpret the Magnus force in terms of the noncommutativity, and obtain some results for the quantum dynamics of the system of vortices in that context.
Combinatorial Dyson-Schwinger equations in noncommutative field theory
Adrian Tanasa; Dirk Kreimer
2009-07-13T23:59:59.000Z
We give here the Hopf algebra structure describing the noncommutative renormalization of a recently introduced translation-invariant model on Moyal space. We define Hochschild one-cocyles $B_+^\\gamma$ which allows us to write down the combinatorial Dyson-Schwinger equations for noncommutative quantum field theory. One- and two-loops examples are explicitly worked out.
Lattice Gauge Fields and Discrete Noncommutative Yang-Mills Theory
J. Ambjorn; Y. M. Makeenko; J. Nishimura; R. J. Szabo
2000-04-21T23:59:59.000Z
We present a lattice formulation of noncommutative Yang-Mills theory in arbitrary even dimensionality. The UV/IR mixing characteristic of noncommutative field theories is demonstrated at a completely nonperturbative level. We prove a discrete Morita equivalence between ordinary Yang-Mills theory with multi-valued gauge fields and noncommutative Yang-Mills theory with periodic gauge fields. Using this equivalence, we show that generic noncommutative gauge theories in the continuum can be regularized nonperturbatively by means of {\\it ordinary} lattice gauge theory with 't~Hooft flux. In the case of irrational noncommutativity parameters, the rank of the gauge group of the commutative lattice theory must be sent to infinity in the continuum limit. As a special case, the construction includes the recent description of noncommutative Yang-Mills theories using twisted large $N$ reduced models. We study the coupling of noncommutative gauge fields to matter fields in the fundamental representation of the gauge group using the lattice formalism. The large mass expansion is used to describe the physical meaning of Wilson loops in noncommutative gauge theories. We also demonstrate Morita equivalence in the presence of fundamental matter fields and use this property to comment on the calculation of the beta-function in noncommutative quantum electrodynamics.
Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation
E. Rico; T. Pichler; M. Dalmonte; P. Zoller; S. Montangero
2014-06-07T23:59:59.000Z
We show that gauge invariant quantum link models, Abelian and non-Abelian, can be exactly described in terms of tensor networks states. Quantum link models represent an ideal bridge between high-energy to cold atom physics, as they can be used in cold-atoms in optical lattices to study lattice gauge theories. In this framework, we characterize the phase diagram of a (1+1)-d quantum link version of the Schwinger model in an external classical background electric field: the quantum phase transition from a charge and parity ordered phase with non-zero electric flux to a disordered one with a net zero electric flux configuration is described by the Ising universality class.
Quadratic $?'$-Corrections to Heterotic Double Field Theory
Kanghoon Lee
2015-04-01T23:59:59.000Z
We investigate $\\alpha'$-corrections of heterotic double field theory up to quadratic order in the language of supersymmetric O(D,D+dim G) gauged double field theory. After introducing double-vielbein formalism with a parametrization which reproduces heterotic supergravity, we show that supersymmetry for heterotic double field theory up to leading order $\\alpha'$-correction is obtained from supersymmetric gauged double field theory. We discuss the necessary modifications of the symmetries defined in supersymmetric gauged double field theory. Further, we construct supersymmetric completion at quadratic order in $\\alpha'$.
Matrix product states for gauge field theories
Boye Buyens; Jutho Haegeman; Karel Van Acoleyen; Henri Verschelde; Frank Verstraete
2014-11-03T23:59:59.000Z
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study non-equilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field.
Do Mixed States save Effective Field Theory from BICEP?
Collins, Hael; Vardanyan, Tereza
2014-01-01T23:59:59.000Z
The BICEP2 collaboration has for the first time observed the B-mode polarization associated with inflationary gravitational waves. Their result has some discomfiting implications for the validity of an effective theory approach to single-field inflation since it would require an inflaton field excursion larger than the Planck scale. We argue that if the quantum state of the gravitons is a mixed state based on the Bunch-Davies vacuum, then the tensor to scalar ratio r measured by BICEP is different than the quantity that enters the Lyth bound. When this is taken into account, the tension between effective field theory and the BICEP result is alleviated.
Do Mixed States save Effective Field Theory from BICEP?
Hael Collins; R. Holman; Tereza Vardanyan
2014-03-21T23:59:59.000Z
The BICEP2 collaboration has for the first time observed the B-mode polarization associated with inflationary gravitational waves. Their result has some discomfiting implications for the validity of an effective theory approach to single-field inflation since it would require an inflaton field excursion larger than the Planck scale. We argue that if the quantum state of the gravitons is a mixed state based on the Bunch-Davies vacuum, then the tensor to scalar ratio r measured by BICEP is different than the quantity that enters the Lyth bound. When this is taken into account, the tension between effective field theory and the BICEP result is alleviated.
The Operator Tensor Formulation of Quantum Theory
Lucien Hardy
2012-01-20T23:59:59.000Z
A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter reading for example), as an operation. An operation can have zero or more quantum systems inputted into it and zero or more quantum systems outputted from it. We can wire together operations to form circuits. In the standard framework of quantum theory we must foliate the circuit then calculate the probability by evolving a state through it. This approach has three problems. First, we must introduce an arbitrary foliation of the circuit (such foliations are not unique). Second, we have to pad our expressions with identities every time two or more foliation hypersurfaces intersect a given wire. And third, we treat operations corresponding to preparations, transformations, and results in different ways. In this paper we present the operator tensor formulation of quantum theory which solves all these problems. Corresponding to every operation is an operator tensor. The probability for a circuit is given by simply replacing the operations in the circuit with the corresponding operator tensors. Wires between operator tensors correspond to multiplying the tensors in the associated subspace and then taking the partial trace over that subspace. Operator tensors must be physical (namely, they must have positive input transpose and satisfy a certain normalization condition).
Interpretation of Stationary States in Prequantum Classical Statistical Field Theory
Andrei Khrennikov
2006-01-26T23:59:59.000Z
We develop a prequantum classical statistical model in that the role of hidden variables is played by classical (vector) fields. We call this model Prequantum Classical Statistical Field Theory (PCSFT). The correspondence between classical and quantum quantities is asymptotic, so we call our approach asymptotic dequantization. In this note we pay the main attention to interpretation of so called pure quantum states (wave functions) in PCSFT, especially stationary states. We show, see Theorem 2, that pure states of QM can be considered as labels for Gaussian measures concentrated on one dimensional complex subspaces of phase space that are invariant with respect to the Schr\\"odinger dynamics. ``A quantum system in a stationary state $\\psi$'' in PCSFT is nothing else than a Gaussian ensemble of classical fields (fluctuations of the vacuum field of a very small magnitude) which is not changed in the process of Schr\\"odinger's evolution. We interpret in this way the problem of {\\it stability of hydrogen atom.
Hamilton-Jacobi theory in k-cosymplectic field theories
M. de León; S. Vilariño
2013-04-11T23:59:59.000Z
In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for time dependent Mechanics to the case of classical field theories in the k-cosymplectic framework.
Field theory on noncommutative spacetimes: Quasiplanar Wick products
Bahns, D.; Fredenhagen, K. [II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, D-22761 Hamburg (Germany); Doplicher, S.; Piacitelli, G. [Dipartimento di Matematica, Universita di Roma 'La Sapienza', Piazzale Aldo Moro 2, 00185 Rome (Italy)
2005-01-15T23:59:59.000Z
We give a definition of admissible counterterms appropriate for massive quantum field theories on the noncommutative Minkowski space, based on a suitable notion of locality. We then define products of fields of arbitrary order, the so-called quasiplanar Wick products, by subtracting only such admissible counterterms. We derive the analogue of Wick's theorem and comment on the consequences of using quasiplanar Wick products in the perturbative expansion.
Natural Philosophy and Quantum Theory
Thomas Marlow
2006-10-25T23:59:59.000Z
We attempt to show how relationalism might help in understanding Bell's theorem. We also present an analogy with Darwinian evolution in order to pedagogically hint at how one might go about using a theory in which one does not even desire to explain correlations by invoking common causes.
Field/source duality in topological field theories
David Delphenich
2007-02-13T23:59:59.000Z
The relationship between the sources of physical fields and the fields themselves is investigated with regard to the coupling of topological information between them. A class of field theories that we call topological field theories is defined such that both the field and its source represent de Rham cocycles in varying dimensions over complementary subspaces and the coupling of one to the other is by way of an isomorphism of the those cohomology spaces, which we refer to as field/source duality. The deeper basis for such an isomorphism is investigated and the process is described for various elementary physical examples of topological field theories.
Topological BF field theory description of topological insulators
Gil Young Cho; Joel E. Moore
2010-12-03T23:59:59.000Z
Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian $BF$ theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The $BF$ description can be motivated from the local excitations produced when a $\\pi$ flux is threaded through this state. For the three-dimensional topological insulator, the $BF$ description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields "axion electrodynamics", i.e., an electromagnetic $E \\cdot B$ term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, $BF$ theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.
Twisting all the way: From classical mechanics to quantum fields
Aschieri, Paolo [Centro Studi e Ricerche 'Enrico Fermi' Compendio Viminale, 00184 Rome (Italy); Dipartimento di Scienze e Tecnologie Avanzate, Universita del Piemonte Orientale, and INFN, Sezione di Torino Via Bellini 25/G 15100 Alessandria (Italy); Lizzi, Fedele; Vitale, Patrizia [Dipartimento di Scienze Fisiche, Universita di Napoli Federico II and INFN, Sezione di Napoli Monte S. Angelo, Via Cintia, 80126 Naples (Italy)
2008-01-15T23:59:59.000Z
We discuss the effects that a noncommutative geometry induced by a Drinfeld twist has on physical theories. We systematically deform all products and symmetries of the theory. We discuss noncommutative classical mechanics, in particular its deformed Poisson bracket and hence time evolution and symmetries. The twisting is then extended to classical fields, and then to the main interest of this work: quantum fields. This leads to a geometric formulation of quantization on noncommutative space-time, i.e., we establish a noncommutative correspondence principle from *-Poisson brackets to * commutators. In particular commutation relations among creation and annihilation operators are deduced.
Magnetic Backgrounds and Noncommutative Field Theory
Richard J. Szabo
2004-02-09T23:59:59.000Z
This paper is a rudimentary introduction, geared at non-specialists, to how noncommutative field theories arise in physics and their applications to string theory, particle physics and condensed matter systems.
Infrared divergence of a scalar quantum field model on a pseudo
Infrared divergence of a scalar quantum field model on a pseudo Riemann manifold Christian G the variable mass is short range, the Hamiltonian has no ground state. Moreover the infrared di- vergence Introduction 1.1 Preliminaries Analysis of the infrared behavior in massless quantum field theory
Entanglement of low-energy excitations in Conformal Field Theory
Francisco Castilho Alcaraz; Miguel Ibanez Berganza; German Sierra
2011-01-28T23:59:59.000Z
In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and Renyi entropies of the ground state, which display a universal logarithmic behaviour depending on the central charge. In this letter we generalize this result to those excited states of the chain that correspond to primary fields in CFT. It is shown that the n-th Renyi entropy is related to a 2n-point correlator of primary fields. We verify this statement for the critical XX and XXZ chains. This result uncovers a new link between quantum information theory and CFT.
Field Definitions, Spectrum and Universality in Effective String Theories
N. D. Hari Dass; Peter Matlock
2006-12-28T23:59:59.000Z
It is shown, by explicit calculation, that the third-order terms in inverse string length in the spectrum of the effective string theories of Polchinski and Strominger are also the same as in Nambu-Goto theory, in addition to the universal Luescher terms. While the Nambu-Goto theory is inconsistent outside the critical dimension, the Polchinski-Strominger theory is by construction consistent for any space-time dimension. In the analysis of the spectrum, care is taken not to use any field redefinition, as it is felt that this has the potential to obscure important points. Nevertheless, as field redefinition is an important tool and the definition of the field should be made precise, a careful analysis of the choice of field definition leading to the terms in the action is also presented. Further, it is shown how a choice of field definition can be made in a systematic way at higher orders. To this end the transformation of measure involved is calculated, in the context of effective string theory, and thereby a quantum evaluation made of equivalence of theories related by a field redefinition. It is found that there are interesting possibilities resulting from a redefinition of fluctuation field.
Two-dimensional topological field theories coupled to four-dimensional BF theory
Merced Montesinos; Alejandro Perez
2007-11-19T23:59:59.000Z
Four dimensional BF theory admits a natural coupling to extended sources supported on two dimensional surfaces or string world-sheets. Solutions of the theory are in one to one correspondence with solutions of Einstein equations with distributional matter (cosmic strings). We study new (topological field) theories that can be constructed by adding extra degrees of freedom to the two dimensional world-sheet. We show how two dimensional Yang-Mills degrees of freedom can be added on the world-sheet, producing in this way, an interactive (topological) theory of Yang-Mills fields with BF fields in four dimensions. We also show how a world-sheet tetrad can be naturally added. As in the previous case the set of solutions of these theories are contained in the set of solutions of Einstein's equations if one allows distributional matter supported on two dimensional surfaces. These theories are argued to be exactly quantizable. In the context of quantum gravity, one important motivation to study these models is to explore the possibility of constructing a background independent quantum field theory where local degrees of freedom at low energies arise from global topological (world-sheet) degrees of freedom at the fundamental level.
Quantum fields with noncommutative target spaces
Balachandran, A. P.; Queiroz, A. R.; Marques, A. M.; Teotonio-Sobrinho, P. [Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (United States); Centro Internacional de Fisica da Materia Condensada, Universidade de Brasilia, C.P. 04667, Brasilia, SP (Brazil); Instituto de Fisica, Universidade de Sao Paulo, C.P. 66318, Sao Paulo, SP, 05315-970 (Brazil)
2008-05-15T23:59:59.000Z
Quantum field theories (QFT's) on noncommutative spacetimes are currently under intensive study. Usually such theories have world sheet noncommutativity. In the present work, instead, we study QFT's with commutative world sheet and noncommutative target space. Such noncommutativity can be interpreted in terms of twisted statistics and is related to earlier work of Oeckl [R. Oeckl, Commun. Math. Phys. 217, 451 (2001).], and others [A. P. Balachandran, G. Mangano, A. Pinzul, and S. Vaidya, Int. J. Mod. Phys. A 21, 3111 (2006); A. P. Balachandran, A. Pinzul, and B. A. Qureshi, Phys. Lett. B 634, 434 (2006); A. P. Balachandran, A. Pinzul, B. A. Qureshi, and S. Vaidya, arXiv:hep-th/0608138; A. P. Balachandran, T. R. Govindarajan, G. Mangano, A. Pinzul, B. A. Qureshi, and S. Vaidya, Phys. Rev. D 75, 045009 (2007); A. Pinzul, Int. J. Mod. Phys. A 20, 6268 (2005); G. Fiore and J. Wess, Phys. Rev. D 75, 105022 (2007); Y. Sasai and N. Sasakura, Prog. Theor. Phys. 118, 785 (2007)]. The twisted spectra of their free Hamiltonians has been found earlier by Carmona et al. [J. M. Carmona, J. L. Cortes, J. Gamboa, and F. Mendez, Phys. Lett. B 565, 222 (2003); J. M. Carmona, J. L. Cortes, J. Gamboa, and F. Mendez, J. High Energy Phys. 03 (2003) 058]. We review their derivation and then compute the partition function of one such typical theory. It leads to a deformed blackbody spectrum, which is analyzed in detail. The difference between the usual and the deformed blackbody spectrum appears in the region of high frequencies. Therefore we expect that the deformed blackbody radiation may potentially be used to compute a Greisen-Zatsepin-Kuzmin cutoff which will depend on the noncommutative parameter {theta}.
Designer Gravity and Field Theory Effective Potentials
Hertog, Thomas; Horowitz, Gary T. [Department of Physics, UCSB, Santa Barbara, California 93106 (United States)
2005-06-10T23:59:59.000Z
Motivated by the anti-de Sitter conformal field theory correspondence, we show that there is remarkable agreement between static supergravity solutions and extrema of a field theory potential. For essentially any function V({alpha}) there are boundary conditions in anti--de Sitter space so that gravitational solitons exist precisely at the extrema of V and have masses given by the value of V at these extrema. Based on this, we propose new positive energy conjectures. On the field theory side, each function V can be interpreted as the effective potential for a certain operator in the dual field theory.
Nuclear forces from chiral effective field theory
R. Machleidt
2007-04-05T23:59:59.000Z
In this lecture series, I present the recent progress in our understanding of nuclear forces in terms of chiral effective field theory.
Symmetries and Renormalization of Noncommutative Field Theory
Szabo, Richard J. [Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS (United Kingdom); Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS (United Kingdom)
2007-06-19T23:59:59.000Z
An overview of recent developments in the renormalization and in the implementation of spacetime symmetries of noncommutative field theory is presented, and argued to be intimately related.
The Quantum Spin Hall Effect: Theory and Experiment
Konig, Markus; Buhmann, Hartmut; Molenkamp, Laurens W.; /Wurzburg U.; Hughes, Taylor L.; /Stanford U., Phys. Dept.; Liu, Chao-Xing; /Tsinghua U., Beijing /Stanford U., Phys. Dept.; Qi, Xiao-Liang; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19T23:59:59.000Z
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the helical edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. Here we review a recent theory which predicts that the QSH state can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the band structure changes from a normal to an 'inverted' type at a critical thickness d{sub c}. We present an analytical solution of the helical edge states and explicitly demonstrate their topological stability. We also review the recent experimental observation of the QSH state in HgTe/(Hg,Cd)Te quantum wells. We review both the fabrication of the sample and the experimental setup. For thin quantum wells with well width d{sub QW} < 6.3 nm, the insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d{sub QW} > 6.3 nm), the nominally insulating regime shows a plateau of residual conductance close to 2e{sup 2}/h. The residual conductance is independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance is destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d{sub c} = 6.3 nm, is also independently determined from the occurrence of a magnetic field induced insulator to metal transition.
Theory of dynamic nuclear polarization and feedback in quantum dots
Sophia E. Economou; Edwin Barnes
2014-04-06T23:59:59.000Z
An electron confined in a quantum dot interacts with its local nuclear spin environment through the hyperfine contact interaction. This interaction combined with external control and relaxation or measurement of the electron spin allows for the generation of dynamic nuclear polarization. The quantum nature of the nuclear bath, along with the interplay of coherent external fields and incoherent dynamics in these systems renders a wealth of intriguing phenomena seen in recent experiments such as electron Zeeman frequency focusing, hysteresis, and line dragging. We develop in detail a fully quantum, self-consistent theory that can be applied to such experiments and that moreover has predictive power. Our theory uses the operator sum representation formalism in order to incorporate the incoherent dynamics caused by the additional, Markovian bath, which in self-assembled dots is the vacuum field responsible for electron-hole optical recombination. The beauty of this formalism is that it reduces the complexity of the problem by encoding the joint dynamics of the external coherent and incoherent driving in an effective dynamical map that only acts on the electron spin subspace. This together with the separation of timescales in the problem allows for a tractable and analytically solvable formalism. The key role of entanglement between the electron spin and the nuclear spins in the formation of dynamic nuclear polarization naturally follows from our solution. We demonstrate the theory in detail for an optical pulsed experiment and present an in-depth discussion and physical explanation of our results.
Nonlocal microscopic theory of quantum friction between parallel metallic slabs
Despoja, Vito [Donostia International Physics Center (DIPC), P. Manuel de Lardizabal, E-20018 San Sebastian, Basque Country (Spain); Department of Physics, University of Zagreb, Bijenicka 32, HR-10000 Zagreb (Croatia); Departamento de Fisica de Materiales and Centro Mixto CSIC-UPV/EHU, Facultad de Ciencias Quimicas, Universidad del Pais Vasco UPV/EHU, Apto. 1072, E-20080 San Sebastian, Basque Country (Spain); Echenique, Pedro M. [Donostia International Physics Center (DIPC), P. Manuel de Lardizabal, E-20018 San Sebastian, Basque Country (Spain); Departamento de Fisica de Materiales and Centro Mixto CSIC-UPV/EHU, Facultad de Ciencias Quimicas, Universidad del Pais Vasco UPV/EHU, Apto. 1072, E-20080 San Sebastian, Basque Country (Spain); Sunjic, Marijan [Donostia International Physics Center (DIPC), P. Manuel de Lardizabal, E-20018 San Sebastian, Basque Country (Spain); Department of Physics, University of Zagreb, Bijenicka 32, HR-10000 Zagreb (Croatia)
2011-05-15T23:59:59.000Z
We present a new derivation of the friction force between two metallic slabs moving with constant relative parallel velocity, based on T=0 quantum-field theory formalism. By including a fully nonlocal description of dynamically screened electron fluctuations in the slab, and avoiding the usual matching-condition procedure, we generalize previous expressions for the friction force, to which our results reduce in the local limit. Analyzing the friction force calculated in the two local models and in the nonlocal theory, we show that for physically relevant velocities local theories using the plasmon and Drude models of dielectric response are inappropriate to describe friction, which is due to excitation of low-energy electron-hole pairs, which are properly included in nonlocal theory. We also show that inclusion of dissipation in the nonlocal electronic response has negligible influence on friction.
From Entropic Dynamics to Quantum Theory
Caticha, Ariel [Department of Physics, University at Albany-SUNY, Albany, NY 12222 (United States)
2009-12-08T23:59:59.000Z
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the configuration space is a statistical manifold. The dynamics then follows from a principle of inference, the method of Maximum Entropy. The concept of time is introduced as a convenient way to keep track of change. The resulting theory resembles both Nelson's stochastic mechanics and general relativity. The statistical manifold is a dynamical entity: its geometry determines the evolution of the probability distribution which, in its turn, reacts back and determines the evolution of the geometry. There is a new quantum version of the equivalence principle: 'osmotic' mass equals inertial mass. Mass and the phase of the wave function are explained as features of purely statistical origin.
Frozen ghosts in thermal gauge field theory
P. V. Landshoff; A. Rebhan
2009-03-10T23:59:59.000Z
We review an alternative formulation of gauge field theories at finite temperature where unphysical degrees of freedom of gauge fields and the Faddeev-Popov ghosts are kept at zero temperature.
Hamiltonian Vector Fields on Multiphase Spaces of Classical Field Theory
Michael Forger; Mário Otávio Salles
2010-10-02T23:59:59.000Z
We present a classification of hamiltonian vector fields on multisymplectic and polysymplectic fiber bundles closely analogous to the one known for the corresponding dual jet bundles that appear in the multisymplectic and polysymplectic approach to first order classical field theories.
Theory for the optimal control of time-averaged quantities in open quantum systems
Ilia Grigorenko; Martin E. Garcia; K. H. Bennemann
2002-03-25T23:59:59.000Z
We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal control field fulfills a high order differential equation, which we solve analytically for some limiting cases. We determine quantitatively how relaxation effects limit the control of the system. The theory is applied to open two level quantum systems. An approximate analytical solution for the level occupations in terms of the applied fields is presented. Different other applications are discussed.
Information Geometry of Entanglement Renormalization for free Quantum Fields
Javier Molina-Vilaplana
2015-05-23T23:59:59.000Z
We provide an explicit connection between the differential generation of entanglement entropy in a tensor network representation of the ground states of two field theories, and a geometric description of these states based on the Fisher information metric. We show how the geometrical description remains invariant despite there is an irreducible gauge freedom in the definition of the tensor network. The results might help to understand how spacetimes may emerge from distributions of quantum states, or more concretely, from the structure of the quantum entanglement concomitant to those distributions.
The spinor field theory of the photon
Ruo Peng Wang
2011-09-18T23:59:59.000Z
I introduce a spinor field theory for the photon. The three-dimensional vector electromagnetic field and the four-dimensional vector potential are components of this spinor photon field. A spinor equation for the photon field is derived from Maxwell's equations,the relations between the electromagnetic field and the four-dimensional vector potential, and the Lorentz gauge condition. The covariant quantization of free photon field is done, and only transverse photons are obtained. The vacuum energy divergence does not occur in this theory. A covariant "positive frequency" condition is introduced for separating the photon field from its complex conjugate in the presence of the electric current and charge.
Topological BF field theory description of topological insulators
Cho, Gil Young [Department of Physics, University of California, Berkeley, CA 94720 (United States); Moore, Joel E., E-mail: jemoore@berkeley.edu [Department of Physics, University of California, Berkeley, CA 94720 (United States); Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)
2011-06-15T23:59:59.000Z
Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac fermion. > The 'axion' term in electromagnetism is correctly obtained from gapped surfaces. > Generalizations to possible fractional phases are discussed in closing. - Abstract: Topological phases of matter are described universally by topological field theories in the same way that symmetry-breaking phases of matter are described by Landau-Ginzburg field theories. We propose that topological insulators in two and three dimensions are described by a version of abelian BF theory. For the two-dimensional topological insulator or quantum spin Hall state, this description is essentially equivalent to a pair of Chern-Simons theories, consistent with the realization of this phase as paired integer quantum Hall effect states. The BF description can be motivated from the local excitations produced when a {pi} flux is threaded through this state. For the three-dimensional topological insulator, the BF description is less obvious but quite versatile: it contains a gapless surface Dirac fermion when time-reversal-symmetry is preserved and yields 'axion electrodynamics', i.e., an electromagnetic E . B term, when time-reversal symmetry is broken and the surfaces are gapped. Just as changing the coefficients and charges of 2D Chern-Simons theory allows one to obtain fractional quantum Hall states starting from integer states, BF theory could also describe (at a macroscopic level) fractional 3D topological insulators with fractional statistics of point-like and line-like objects.
Stochastic Dynamics of Coarse-Grained Quantum Fields in Inflationary Universe
Milan Mijic
1994-01-26T23:59:59.000Z
It is shown how coarse-graining of quantum field ^M theory in de Sitter space leads to the emergence of a classical ^M stochastic description as an effective theory in the infra-red regime. ^M The quantum state of the coarse-grained scalar field is found to be a highly^M squeezed coherent state, whose center performs a random walk on a^M bundle of classical trajectories.^M
Uniform Theory of Multiplicative Valued Difference Fields
Pal, Koushik
2011-01-01T23:59:59.000Z
and M ODDAG are co-theories (see Definition 2.1.28). We alsoof model companion (see Definition 2.1.28) of a theory is anValuation Theory Valued Fields Definition 2.3.1. A triple K
The Poisson algebra of classical Hamiltonians in field theory and the problem of its quantization
A. Stoyanovsky
2010-10-20T23:59:59.000Z
We construct the commutative Poisson algebra of classical Hamiltonians in field theory. We pose the problem of quantization of this Poisson algebra. We also make some interesting computations in the known quadratic part of the quantum algebra.
D-Branes in Noncommutative Field Theory
Richard J. Szabo
2007-05-08T23:59:59.000Z
A mathematical introduction to the classical solutions of noncommutative field theory is presented, with emphasis on how they may be understood as states of D-branes in Type II superstring theory. Both scalar field theory and gauge theory on Moyal spaces are extensively studied. Instantons in Yang-Mills theory on the two-dimensional noncommutative torus and the fuzzy sphere are also constructed. In some instances the connection to D-brane physics is provided by a mapping of noncommutative solitons into K-homology.
Symmetries in k-Symplectic Field Theories
Roman-Roy, Narciso [Departamento de Matematica Aplicada IV. Edificio C-3, Campus Norte UPC, C/Jordi Girona 1.08034 Barcelona (Spain); Salgado, Modesto; Vilarino, Silvia [Departamento de Xeometria e Topoloxia, Facultade de Matematicas, Universidade de Santiago de Compostela. 15782 Santiago de Compostela (Spain)
2008-06-25T23:59:59.000Z
k-symplectic geometry provides the simplest geometric framework for describing certain class of first-order classical field theories. Using this description we analyze different kinds of symmetries for the Hamiltonian and Lagrangian formalisms of these field theories, including the study of conservation laws associated to them and stating Noether's theorem.
Classical field theory. Advanced mathematical formulation
G. Sardanashvily
2009-03-04T23:59:59.000Z
In contrast with QFT, classical field theory can be formulated in strict mathematical terms of fibre bundles, graded manifolds and jet manifolds. Second Noether theorems provide BRST extension of this classical field theory by means of ghosts and antifields for the purpose of its quantization.
Noncommutative Field Theory and Lorentz Violation
Sean M. Carroll; Jeffrey A. Harvey; V. Alan Kostelecky; Charles D. Lane; Takemi Okamoto
2001-05-09T23:59:59.000Z
The role of Lorentz symmetry in noncommutative field theory is considered. Any realistic noncommutative theory is found to be physically equivalent to a subset of a general Lorentz-violating standard-model extension involving ordinary fields. Some theoretical consequences are discussed. Existing experiments bound the scale of the noncommutativity parameter to (10 TeV)^{-2}.
Noncommutative Field Theory and Lorentz Violation
Carroll, Sean M.; Harvey, Jeffrey A.; Kostelecky, V. Alan; Lane, Charles D.; Okamoto, Takemi
2001-10-01T23:59:59.000Z
The role of Lorentz symmetry in noncommutative field theory is considered. Any realistic noncommutative theory is found to be physically equivalent to a subset of a general Lorentz-violating standard-model extension involving ordinary fields. Some theoretical consequences are discussed. Existing experiments bound the scale of the noncommutativity parameter to (10 TeV){sup -2} .
The EMC effect in effective field theory
Detmold, William [Department of Physics, Box 351560, University of Washington, Seattle, WA 98195 (United States)
2005-10-06T23:59:59.000Z
Using effective field theory, we investigate nuclear modification of nucleon parton distributions (for example, the EMC effect). We show that the universality of the shape distortion in nuclear parton distributions (the factorisation of the Bjorken x and atomic number (A) dependence) is model independent and emerges naturally in effective field theory. We present simple fits to experimental data that incorporate this factorisation.
On Fusion Rules in Logarithmic Conformal Field Theories
Michael Flohr
1996-06-10T23:59:59.000Z
We find the fusion rules for the c_{p,1} series of logarithmic conformal field theories. This completes our attempts to generalize the concept of rationality for conformal field theories to the logarithmic case. A novelty is the appearance of negative fusion coefficients which can be understood in terms of exceptional quantum group representations. The effective fusion rules (i.e. without signs and multiplicities) resemble the BPZ fusion rules for the virtual minimal models with conformal grid given via c = c_{3p,3}. This leads to the conjecture that (almost) all minimal models with c = c_{p,q}, gcd(p,q) > 1, belong to the class of rational logarithmic conformal field theories.
Chiral field theory of $0^{-+}$ glueball
Bing an Li
2010-02-22T23:59:59.000Z
A chiral field theory of $0^{-+}$ glueball is presented. By adding a $0^{-+}$ glueball field to a successful Lagrangian of chiral field theory of pseudoscalar, vector, and axial-vector mesons, the Lagrangian of this theory is constructed. The couplings between the pseodoscalar glueball field and mesons are via U(1) anomaly revealed. Qualitative study of the physical processes of the $0^{-+}$ glueball of $m=1.405\\textrm{GeV}$ is presented. The theoretical predictions can be used to identify the $0^{-+}$ glueball.
Unified field theories and Einstein
S C Tiwari
2006-02-16T23:59:59.000Z
Einstein's contribution to relativity is reviewed. It is pointed out that Weyl gave first unified theory of gravitation and electromagnetism and it was different than the five dimensional theory of Kaluza. Einstein began his work on unification in 1925 that continued whole through the rest of his life.
Scattering Theory for Open Quantum Systems
J. Behrndt; M. M. Malamud; H. Neidhardt
2006-10-31T23:59:59.000Z
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator $A_D$ in a Hilbert space $\\sH$ is used to describe an open quantum system. In this case the minimal self-adjoint dilation $\\widetilde K$ of $A_D$ can be regarded as the Hamiltonian of a closed system which contains the open system $\\{A_D,\\sH\\}$, but since $\\widetilde K$ is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family $\\{A(\\mu)\\}$ of maximal dissipative operators depending on energy $\\mu$, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single Pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative and quantum transmitting Schr\\"{o}dinger-Poisson systems.
Atomic Probes of Noncommutative Field Theory
Charles D. Lane
2002-01-07T23:59:59.000Z
We consider the role of Lorentz symmetry in noncommutative field theory. We find that a Lorentz-violating standard-model extension involving ordinary fields is general enough to include any realisitc noncommutative field theory as a subset. This leads to various theoretical consequences, as well as bounds from existing experiments at the level of (10 TeV)$^{-2}$ on the scale of the noncommutativity parameter.
M5-brane defect and quantum Hall effect in AdS{sub 4}xN(1,1)/N=3 superconformal field theory
Fujita, Mitsutoshi [Department of Physics, Kyoto University, Kyoto 606-8502 (Japan)
2011-05-15T23:59:59.000Z
We study the d=11 gravity dual AdS{sub 4}xN(1,1) of the d=3 N=3 flavored Chern-Simons-matter theory. In the dual gravity side, we analyze the M5-brane filling AdS{sub 3} inside AdS{sub 4} and derive the quantized Hall conductivity of the dual gauge theory. In the gauge theory side, this M5-brane intersects the gauge theory at the codimension-one defect.
Fermions in spherical field theory
Dean Lee
1999-01-07T23:59:59.000Z
We derive the spherical field formalism for fermions. We find that the spherical field method is free from certain difficulties which complicate lattice calculations, such as fermion doubling, missing axial anomalies, and computational problems regarding internal fermion loops.
Analogy between turbulence and quantum gravity: beyond Kolmogorov's 1941 theory
S. Succi
2011-11-14T23:59:59.000Z
Simple arguments based on the general properties of quantum fluctuations have been recently shown to imply that quantum fluctuations of spacetime obey the same scaling laws of the velocity fluctuations in a homogeneous incompressible turbulent flow, as described by Kolmogorov 1941 (K41) scaling theory. Less noted, however, is the fact that this analogy rules out the possibility of a fractal quantum spacetime, in contradiction with growing evidence in quantum gravity research. In this Note, we show that the notion of a fractal quantum spacetime can be restored by extending the analogy between turbulence and quantum gravity beyond the realm of K41 theory. In particular, it is shown that compatibility of a fractal quantum-space time with the recent Horava-Lifshitz scenario for quantum gravity, implies singular quantum wavefunctions. Finally, we propose an operational procedure, based on Extended Self-Similarity techniques, to inspect the (multi)-scaling properties of quantum gravitational fluctuations.
Modified Ostrogradski formulation of field theory
M. Leclerc
2007-02-27T23:59:59.000Z
We present a method for the Hamiltonian formulation of field theories that are based on Lagrangians containing second derivatives. The new feature of our formalism is that all four partial derivatives of the field variables are initially considered as independent fields, in contrast to the conventional Ostrogradski method, where only the velocity is turned into an independent field variable. The consistency of the formalism is demonstrated by simple unconstrained and constrained second order scalar field theories. Its application to General Relativity is briefly outlined.
Introduction to conformal field theory and string theory
Dixon, L.J.
1989-12-01T23:59:59.000Z
These lectures are meant to provide a brief introduction to conformal field theory (CFT) and string theory for those with no prior exposure to the subjects. There are many excellent reviews already available, and most of these go in to much more detail than I will be able to here. 52 refs., 11 figs.
Open quantum systems and Random Matrix Theory
Declan Mulhall
2015-01-09T23:59:59.000Z
A simple model for open quantum systems is analyzed with Random Matrix Theory. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the $\\Delta_3(L)$ statistic, width distribution and level spacing are examined as a function of the strength of this coupling. A super-radiant transition is observed, and it is seen that as it is formed, the level spacing and $\\Delta_3(L)$ statistic exhibit the signatures of missed levels.
Thermal Correlation Functions of Twisted Quantum Fields
Prasad Basu; Rahul Srivastava; Sachindeo Vaidya
2010-04-08T23:59:59.000Z
We derive the thermal correlators for twisted quantum fields on noncommutative spacetime. We show that the thermal expectation value of the number operator is same as in commutative spacetime, but that higher correlators are sensitive to the noncommutativity parameters $\\theta^{\\mu\
Thermal correlation functions of twisted quantum fields
Basu, Prasad; Srivastava, Rahul; Vaidya, Sachindeo [Centre for High Energy Physics, Indian Institute of Science, Bangalore, 560012 (India)
2010-07-15T23:59:59.000Z
We derive the thermal correlators for twisted quantum fields on noncommutative spacetime. We show that the thermal expectation value of the number operator is same as in commutative spacetime, but that higher correlators are sensitive to the noncommutativity parameters {theta}{sup {mu}{nu}.}
Hamilton-Jacobi theory in multisymplectic classical field theories
Manuel de León; Pedro Daniel Prieto-Martínez; Narciso Román-Roy; Silvia Vilariño
2015-04-08T23:59:59.000Z
The geometric framework for the Hamilton-Jacobi theory developed in previous works is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results.
Effective field theories for inclusive B decays
Lee, Keith S. M. (Keith Seng Mun)
2006-01-01T23:59:59.000Z
In this thesis, we study inclusive decays of the B meson. These allow one to determine CKM elements precisely and to search for physics beyond the Standard Model. We use the framework of effective field theories, in ...
Double field theory of type II strings
Hohm, Olaf
We use double field theory to give a unified description of the low energy limits of type IIA and type IIB superstrings. The Ramond-Ramond potentials fit into spinor representations of the duality group O(D, D) and ...
Nuclear clusters with Halo Effective Field Theory
Renato Higa
2008-09-30T23:59:59.000Z
After a brief discussion of effective field theory applied to nuclear clusters, I present the aspect of Coulomb interactions, with applications to low-energy alpha-alpha and nucleon-alpha scattering.
Operatorial Methods in Noncommutative Field Theory
Acatrinei, Ciprian [Smoluchowski Institute of Physics, Jagellonian University Reymonta 4, Cracow (Poland)
2007-11-14T23:59:59.000Z
We review the operatorial quantization of noncommutative field theory, with emphasis on the fundamentally bilocal nature of the degrees of freedom. Interactions and IR/UV mixing are discussed from this point of view.
A Count of Classical Field Theory Graphs
Gordon Chalmers
2005-07-28T23:59:59.000Z
A generating function is derived that counts the number of diagrams in an arbitrary scalar field theory. The number of graphs containing any number $n_j$ of $j$-point vertices is given. The count is also used to obtain the number of classical graphs in gauge theory and gravity.
Open Systems Dynamics for Propagating Quantum Fields
Ben Q. Baragiola
2014-08-18T23:59:59.000Z
In this dissertation, I explore interactions between matter and propagating light. The electromagnetic field is modeled as a reservoir of quantum harmonic oscillators successively streaming past a quantum system. Each weak and fleeting interaction entangles the light and the system, and the light continues its course. Within the framework of open quantum systems, the light is eventually traced out, leaving the reduced quantum state of the system as the primary mathematical subject. Two major results are presented. The first is a master equation approach for a quantum system interacting with a traveling wave packet prepared with a definite number of photons. In contrast to quasi-classical states, such as coherent or thermal fields, these N-photon states possess temporal mode entanglement, and local interactions in time have nonlocal consequences. The second is a model for a three-dimensional light-matter interface for an atomic ensemble interacting with a paraxial laser beam and its application to the generation of QND spin squeezing. Both coherent and incoherent dynamics due to spatially inhomogeneous atom-light coupling across the ensemble are accounted for. Measurement of paraxially scattered light can generate squeezing of an atomic spin wave, while diffusely scattered photons lead to spatially local decoherence.
Effective Field Theory Techniques for Resummation in Jet Physics
Dunn, Nicholas Daniel
2012-01-01T23:59:59.000Z
gamma in effective field theory. Phys. Rev. , D63:014006, [factorization from effective field theory. Phys. Rev. , D66:Stewart. An ef- fective field theory for collinear and soft
Classical and quantum Big Brake cosmology for scalar field and tachyonic models
Kamenshchik, A. Yu. [Dipartimento di Fisica e Astronomia and INFN, Via Irnerio 46, 40126 Bologna (Italy) and L.D. Landau Institute for Theoretical Physics of the Russian Academy of Sciences, Kosygin str. 2, 119334 Moscow (Russian Federation); Manti, S. [Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa (Italy)
2013-02-21T23:59:59.000Z
We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bang and Big Crunch singularities are not traversable.
Weak Gravity Conjecture for Noncommutative Field Theory
Qing-Guo Huang; Jian-Huang She
2006-11-20T23:59:59.000Z
We investigate the weak gravity bounds on the U(1) gauge theory and scalar field theories in various dimensional noncommutative space. Many results are obtained, such as the upper bound on the noncommutative scale $g_{YM}M_p$ for four dimensional noncommutative U(1) gauge theory. We also discuss the weak gravity bounds on their commutative counterparts. For example, our result on 4 dimensional noncommutative U(1) gauge theory reduces in certain limit to its commutative counterpart suggested by Arkani-Hamed et.al at least at tree-level.
Nonlocal regularisation of noncommutative field theories
T. R. Govindarajan; Seckin Kurkcuoglu; Marco Panero
2006-05-01T23:59:59.000Z
We study noncommutative field theories, which are inherently nonlocal, using a Poincar\\'e-invariant regularisation scheme which yields an effective, nonlocal theory for energies below a cut-off scale. After discussing the general features and the peculiar advantages of this regularisation scheme for theories defined in noncommutative spaces, we focus our attention onto the particular case when the noncommutativity parameter is inversely proportional to the square of the cut-off, via a dimensionless parameter $\\eta$. We work out the perturbative corrections at one-loop order for a scalar theory with quartic interactions, where the signature of noncommutativity appears in $\\eta$-dependent terms. The implications of this approach, which avoids the problems related to UV-IR mixing, are discussed from the perspective of the Wilson renormalisation program. Finally, we remark about the generality of the method, arguing that it may lead to phenomenologically relevant predictions, when applied to realistic field theories.
Space-Time Noncommutative Field Theories And Unitarity
Jaume Gomis; Thomas Mehen
2000-08-01T23:59:59.000Z
We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space-time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This can be understood from string theory, since space noncommutative field theories describe a low energy limit of string theory in a background magnetic field. On the other hand, there is no regime in which space-time noncommutative field theory is an appropriate description of string theory. Whenever space-time noncommutative field theory becomes relevant massive open string states cannot be neglected.
D-branes and string field theory
Sigalov, Ilya
2006-01-01T23:59:59.000Z
In this thesis we study the D-brane physics in the context of Witten's cubic string field theory. We compute first few terms the low energy effective action for the non-abelian gauge field A, from Witten's action. We show ...
Chiral effective field theory and nuclear forces
R. Machleidt; D. R. Entem
2011-05-15T23:59:59.000Z
We review how nuclear forces emerge from low-energy QCD via chiral effective field theory. The presentation is accessible to the non-specialist. At the same time, we also provide considerable detailed information (mostly in appendices) for the benefit of researchers who wish to start working in this field.
An additive Hamiltonian plus Landauer's Principle yields quantum theory
Chris Fields
2015-03-27T23:59:59.000Z
It is shown that no-signalling, a quantum of action, unitarity, detailed balance, Bell's theorem, the Hilbert-space representation of physical states and the Born rule all follow from the assumption of an additive Hamiltonian together with Landauer's principle. Common statements of the "classical limit" of quantum theory, as well as common assumptions made by "interpretations" of quantum theory, contradict additivity, Landauer's principle, or both.
Dynamical Wave Function Collapse Models in Quantum Measure Theory
Fay Dowker; Yousef Ghazi-Tabatabai
2008-05-15T23:59:59.000Z
The structure of Collapse Models is investigated in the framework of Quantum Measure Theory, a histories-based approach to quantum mechanics. The underlying structure of coupled classical and quantum systems is elucidated in this approach which puts both systems on a spacetime footing. The nature of the coupling is exposed: the classical histories have no dynamics of their own but are simply tied, more or less closely, to the quantum histories.
Quasi-probability representations of quantum theory with applications to quantum information science
Christopher Ferrie
2011-10-15T23:59:59.000Z
This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional quantum theory. We focus on both the characteristics and applications of these representations with an emphasis toward quantum information theory. We discuss the recently proposed unification of the set of possible quasi-probability representations via frame theory and then discuss the practical relevance of negativity in such representations as a criteria for quantumness.
Limited Holism and Real-Vector-Space Quantum Theory
Lucien Hardy; William K. Wootters
2010-05-26T23:59:59.000Z
Quantum theory has the property of "local tomography": the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We consider in this paper a class of theories more holistic than quantum theory in that they are constrained only by "bilocal tomography": the state of any composite system is determined by the statistics of measurements on pairs of components. Under a few auxiliary assumptions, we derive certain general features of such theories. In particular, we show how the number of state parameters can depend on the number of perfectly distinguishable states. We also show that real-vector-space quantum theory, while not locally tomographic, is bilocally tomographic.
Operational quantum theory without predefined time
Ognyan Oreshkov; Nicolas J. Cerf
2014-12-25T23:59:59.000Z
The current operational formulation of quantum theory is based on the concept of operation with an input and an output system, which assumes a prior notion of time and is asymmetric under time reversal. But in certain contexts, such as those involving gravity, time is expected to be dynamical and not predefined. Here, we propose an operational formulation of quantum theory without any predefined notion of time. It is based on a generalization of the concept of operation motivated by an epistemic approach: an operation is a description of knowledge about the events in a given region, which can be updated conditionally on information obtained from that region. Each such region has a set of boundary systems, which by definition provide the sole means of information exchange between the events in the region and the events in other regions. Separate operations can be connected in networks through their boundary systems with no directionality assumed for the connections, which generalizes the standard circuit picture. The events associated with an operation are described by positive semidefinite operators on the Hilbert spaces of the boundary systems, while the connections between regions are described by entangled states that encode a nontrivial physical symmetry. A simple rule provides the joint probabilities for the events in a network of operations. We discuss how it may be possible to understand the emergence of a causal structure from properties of the operators on the boundaries of compact space-time regions. The framework allows for indefinite causal order, timelike loops, and other acausal structures. As part of this work, we obtain a generalization of Wigner's theorem, which is based on the preservation of probabilities of actual events and thus puts the concept of time reversal symmetry on operational grounds. It contains the possibility for a new class of symmetry transformations.
Selected Issues in Thermal Field Theory
Chihiro Sasaki
2014-08-04T23:59:59.000Z
New developments on hot and dense QCD in effective field theories are reviewed. Recent investigations in lattice gauge theories for the low-lying Dirac eigenmodes suggest survival hadrons in restored phase of chiral symmetry. We discuss expected properties of those bound states in a medium using chiral approaches. The role of higher-lying hadrons near chiral symmetry restoration is also argued from the conventional and the holographic point of view.
A CSP Field Theory with Helicity Correspondence
Philip Schuster; Natalia Toro
2014-04-02T23:59:59.000Z
We propose the first covariant local action describing the propagation of a single free continuous-spin degree of freedom. The theory is simply formulated as a gauge theory in a "vector superspace", but can also be formulated in terms of a tower of symmetric tensor gauge fields. When the spin invariant $\\rho$ vanishes, the helicity correspondence is manifest -- familiar gauge theory actions are recovered and couplings to conserved currents can easily be introduced. For non-zero $\\rho$, a tower of tensor currents must be present, of which only the lowest rank is exactly conserved. A paucity of local gauge-invariant operators for non-zero $\\rho$ suggests that the equations of motion in any interacting theory should be covariant, not invariant, under a generalization of the free theory's gauge symmetry.
Chu, Shih-I; Tietz, James V.; Datta, Krishna K.
1982-01-01T23:59:59.000Z
of the HF molecule as functions of field strengths and frequency. Nonlinear effects such as power broadening, dynamic Stark shift, Autler–Townes multiplet splitting, hole burning, and S?hump behaviors, etc., are observed and discussed in terms of quasienergy...
Quantum Limit on Stability of Clocks in a Gravitational Field
Supurna Sinha; Joseph Samuel
2014-03-21T23:59:59.000Z
Good clocks are of importance both to fundamental physics and for applications in astronomy, metrology and global positioning systems. In a recent technological breakthrough, researchers at NIST have been able to achieve a stability of 1 part in $10^{18}$ using an Ytterbium clock. This naturally raises the question of whether there are fundamental limits to the stability of clocks. In this paper we point out that gravity and quantum mechanics set a fundamental limit on the stability of clocks. This limit comes from a combination of the uncertainty relation, the gravitational redshift and the relativistic time dilation effect. For example, a single ion hydrogen maser clock in a terrestrial gravitational field cannot achieve a stability better than one part in $10^{22}$. This observation has implications for laboratory experiments involving both gravity and quantum theory.
Limiting the complexity of quantum states: a toy theory
Valerio Scarani
2015-03-30T23:59:59.000Z
This paper discusses a restriction of quantum theory, in which very complex states would be excluded. The toy theory is phrased in the language of the circuit model for quantum computing, its key ingredient being a limitation on the number of interactions that \\textit{each} qubit may undergo. As long as one stays in the circuit model, the toy theory is consistent and may even match what we shall be ever able to do in a controlled laboratory experiment. The direct extension of the restriction beyond the circuit model conflicts with observed facts: the possibility of restricting the complexity of quantum state, while saving phenomena, remains an open question.
Z Theory and its Quantum-Relativistic Operators
Pietro Giorgio Zerbo
2006-02-08T23:59:59.000Z
The view provided by Z theory, based on its quantum-relativistic operators, is an integrated picture of the micro and macro quantities relationships. The axiomatic formulation of the theory is presented in this paper. The theory starts with the existence of the wave function, the existence of three fundamental constants h, c and G as well as the physical quantity Rc (the radius of the space-time continuum) plus the definition of a general form for the quantum-relativistic functional operators. Using such starting point the relationships between relativity, quantum mechanics and cosmological quantities can be clarified.
Extended Hamiltonian systems in multisymplectic field theories
Echeverria-Enriquez, Arturo; Leon, Manuel de; Munoz-Lecanda, Miguel C.; Roman-Roy, Narciso [Departamento de Matematica Aplicada IV, Campus Norte UPC, Edificio C-3, C/Jordi Girona 1, E-08034 Barcelona (Spain); Instituto de Matematicas y Fisica Fundamental, CSIC, C/Serrano 123, E-28006 Madrid (Spain); Departamento de Matematica Aplicada IV, Campus Norte UPC, Edificio C-3, C/Jordi Girona 1, E-08034 Barcelona (Spain)
2007-11-15T23:59:59.000Z
We consider Hamiltonian systems in first-order multisymplectic field theories. We review the properties of Hamiltonian systems in the so-called restricted multimomentum bundle, including the variational principle which leads to the Hamiltonian field equations. In an analogous way to how these systems are defined in the so-called extended (symplectic) formulation of nonautonomous mechanics, we introduce Hamiltonian systems in the extended multimomentum bundle. The geometric properties of these systems are studied, the Hamiltonian equations are analyzed using integrable multivector fields, the corresponding variational principle is also stated, and the relation between the extended and the restricted Hamiltonian systems is established. All these properties are also adapted to certain kinds of submanifolds of the multimomentum bundles in order to cover the case of almost-regular field theories.
Quantum mechanical observer and superstring/M theory
M. Dance
2008-12-31T23:59:59.000Z
Terms are suggested for inclusion in a Lagrangian density as seen by an observer O2, to represent the dynamics of a quantum mechanical observer O1 that is an initial stage in an observation process. This paper extends an earlier paper which suggested that the centre-of-mass kinetic energy of O1 could correspond to, and possibly underlie, the Lagrangian density for bosonic string theory, where the worldsheet coordinates are the coordinates which O1 can observe. The present paper considers a fermion internal to O1, in addition to O1's centre of mass. It is suggested that quantum mechanical uncertainties in the transformation between O1's and O2's reference systems might require O2 to use $d$ spinor fields for this fermion, where $d$ is the number of spacetime dimensions. If this is the case, and if the symmetry/observability arguments in arXiv:hep-th/0601104 apply, the resulting Lagrangian density for the dynamics of O1 might resemble, or even underlie, superstring/M theory.
Coadjoint Orbits and Conformal Field Theory
Washington Taylor IV
1993-10-11T23:59:59.000Z
This thesis describes a new approach to conformal field theory. This approach combines the method of coadjoint orbits with resolutions and chiral vertex operators to give a construction of the correlation functions of conformal field theories in terms of geometrically defined objects. Explicit formulae are given for representations of Virasoro and affine algebras in terms of a local gauge choice on the line bundle associated with geometric quantization of a given coadjoint orbit; these formulae define a new set of explicit bosonic realizations of these algebras. The coadjoint orbit realizations take the form of dual Verma modules, making it possible to avoid the technical difficulties associated with the two-sided resolutions which arise from Feigin-Fuchs and Wakimoto realizations. Formulae are given for screening and intertwining operators on the coadjoint orbit representations. Chiral vertex operators between Virasoro modules are constructed, and related directly to Virasoro algebra generators in certain cases. From the point of view taken in this thesis, vertex operators have a geometric interpretation as differential operators taking sections of one line bundle to sections of another. A suggestion is made that by connecting this description with recent work deriving field theory actions from coadjoint orbits, a deeper understanding of the geometry of conformal field theory might be achieved.
Fusion rules in conformal field theory
J. Fuchs
1993-07-09T23:59:59.000Z
Several aspects of fusion rings and fusion rule algebras, and of their manifestations in twodimensional (conformal) field theory, are described: diagonalization and the connection with modular invariance; the presentation in terms of quotients of polynomial rings; fusion graphs; various strategies that allow for a partial classification; and the role of the fusion rules in the conformal bootstrap programme.
Modular bootstrap in Liouville field theory
Leszek Hadasz; Zbigniew Jaskolski; Paulina Suchanek
2009-11-22T23:59:59.000Z
The modular matrix for the generic 1-point conformal blocks on the torus is expressed in terms of the fusion matrix for the 4-point blocks on the sphere. The modular invariance of the toric 1-point functions in the Liouville field theory with DOZZ structure constants is proved.
Effective Field Theory and Finite Density Systems
R. J. Furnstahl; G. Rupak; T. Schaefer
2008-01-04T23:59:59.000Z
This review gives an overview of effective field theory (EFT) as applied at finite density, with a focus on nuclear many-body systems. Uniform systems with short-range interactions illustrate the ingredients and virtues of many-body EFT and then the varied frontiers of EFT for finite nuclei and nuclear matter are surveyed.
Supersymmetric Field Theories on Noncommutative Spaces
Yoshinobu Habara
2002-05-07T23:59:59.000Z
Supersymmetric field theories on noncommutative spaces are constructed. We present two different representations of noncommutative space, but we can obtain supersymmetry algebla and supersymmetric Yang-Mills action independent of its representation. As a result, we will see that the action has a close relationship with IIB matrix model.
Field Theory Approaches to Nonequilibrium Dynamics
Täuber, Uwe Claus
0435, USA email: tauber@vt.edu Financial support: National Science Foundation, Division of Materials September 2005 i #12; Lecture I: Critical dynamics 1. Introduction: critical slowing down 2. Field theory, critical exponents 5. Critical dynamics with reversible modecouplings 6. Critical relaxation, initial slip
Lifshitz field theories, Snyder noncomutative space-time and momentum dependent metric
Romero, Juan M
2015-01-01T23:59:59.000Z
In this work, we propose three different modified relativistic particles. In the first case, we propose a particle with metrics depending on the momenta and we show that the quantum version of these systems includes different field theories, as anisotropic field theories. As a second case we propose a particle that implies a modified symplectic structure and we show that the quantum version of this system gives different noncommutative space-times, for example the Snyder space-time. In the third case, we combine both structures before mentioned, namely noncommutative space-times and momentum dependent metrics. In this last case, we show that anisotropic field theories can be seen as a limit of no commutative field theory.
Completely Reducible maps in Quantum Information Theory
Daniel Cariello
2015-02-18T23:59:59.000Z
In order to compute the Schmidt decomposition of $A\\in M_k\\otimes M_m$, we must consider an associated self-adjoint map. Here, we show that if $A$ is positive under partial transposition (PPT) or symmetric with positive coefficients (SPC) or invariant under realignment then its associated self-adjoint map is completely reducible. We give applications of this fact in Quantum Information Theory. We recover some theorems recently proved for PPT and SPC matrices and we prove these theorems for matrices invariant under realignment using theorems of Perron-Frobenius theory. We also provide a new proof of the fact that if $\\mathbb{C}^{k}$ contains $k$ mutually unbiased bases then $\\mathbb{C}^{k}$ contains $k+1$. We search for other types of matrices that could have the same property. We consider a group of linear transformations acting on $M_k\\otimes M_k$, which contains the partial transpositions and the realignment map. For each element of this group, we consider the set of matrices in $M_k\\otimes M_k\\simeq M_{k^2}$ that are positive and remain positive, or invariant, under the action of this element. Within this family of sets, we have the set of PPT matrices, the set of SPC matrices and the set of matrices invariant under realignment. We show that these three sets are the only sets of this family such that the associated self-adjoint map of each matrix is completely reducible. We also show that every matrix invariant under realignment is PPT in $M_2\\otimes M_2$ and we present a counterexample in $M_k\\otimes M_k$, $k\\geq 3$.
Confluent primary fields in the conformal field theory
Hajime Nagoya; Juanjuan Sun
2010-08-23T23:59:59.000Z
For any complex simple Lie algebra, we generalize primary fileds in the Wess-Zumino-Novikov-Witten conformal field theory with respect to the case of irregular singularities and we construct integral representations of hypergeometric functions of confluent type, as expectation values of products of generalized primary fields. In the case of sl(2), these integral representations coincide with solutions to confluent KZ equations. Computing the operator product expansion of the energy-momentum tensor and the generalized primary field, new differential operators appear in the result. In the case of sl(2), these differential operators are the same as those of the confluent KZ equations.
Exterior Differential Systems for Field Theories
Estabrook, Frank B
2014-01-01T23:59:59.000Z
Cartan forms and Exterior Differential Systems, set in the state space of field and potential variables taken together with four space-time variables, are formulated for Maxwell, SU(2), SU(3) and SU(4) classical gauge theories minimally coupled to Dirac spinor multiplets. Their Cartan character tables are calculated, showing the EDS, and so the Euler-Lagrange partial differential equations, of the first of these to be well posed. That theory anticipates QED. In the other cases, only if the Dirac fields' conserved currents are suppressed as sources for the Yang-Mills fields is a well posed EDS found. PACS numbers: 02.30.Xx 02.40.Hw 03.50.De 03.50.-z
Bilinear covariants and spinor fields duality in quantum Clifford algebras
Ab?amowicz, Rafa?, E-mail: rablamowicz@tntech.edu [Department of Mathematics, Box 5054, Tennessee Technological University, Cookeville, Tennessee 38505 (United States); Gonçalves, Icaro, E-mail: icaro.goncalves@ufabc.edu.br [Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, 05508-090, São Paulo, SP (Brazil); Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170 Santo André, SP (Brazil); Rocha, Roldão da, E-mail: roldao.rocha@ufabc.edu.br [Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170 Santo André, SP (Brazil); International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste (Italy)
2014-10-15T23:59:59.000Z
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying Z-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, “The unpredictability of quantum gravity,” Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.
Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference
Guido Bacciagaluppi; Antony Valentini
2009-10-24T23:59:59.000Z
We reconsider the crucial 1927 Solvay conference in the context of current research in the foundations of quantum theory. Contrary to folklore, the interpretation question was not settled at this conference and no consensus was reached; instead, a range of sharply conflicting views were presented and extensively discussed. Today, there is no longer an established or dominant interpretation of quantum theory, so it is important to re-evaluate the historical sources and keep the interpretation debate open. In this spirit, we provide a complete English translation of the original proceedings (lectures and discussions), and give background essays on the three main interpretations presented: de Broglie's pilot-wave theory, Born and Heisenberg's quantum mechanics, and Schroedinger's wave mechanics. We provide an extensive analysis of the lectures and discussions that took place, in the light of current debates about the meaning of quantum theory. The proceedings contain much unexpected material, including extensive discussions of de Broglie's pilot-wave theory (which de Broglie presented for a many-body system), and a "quantum mechanics" apparently lacking in wave function collapse or fundamental time evolution. We hope that the book will contribute to the ongoing revival of research in quantum foundations, as well as stimulate a reconsideration of the historical development of quantum physics. A more detailed description of the book may be found in the Preface. (Copyright by Cambridge University Press (ISBN: 9780521814218).)
A holographic model for antiferromagnetic quantum phase transition induced by magnetic field
Rong-Gen Cai; Run-Qiu Yang; F. V. Kusmartsev
2015-01-19T23:59:59.000Z
We propose a gravity dual of antiferromagnetic quantum phase transition (QPT) induced by magnetic field and study the criticality in the vicinity of quantum critical point (QCP). Results show the boundary critical theory is a strong coupling theory with dynamic exponent $z=2$. The hyperscaling law is violated and logarithmic corrections appear near the QCP. We compare our theoretical results with experimental data on variety of materials including low-dimensional magnet, BiCoPO$_5$ and pyrochlores, Er$_{2-2x}$Y$_{2x}$Ti$_2$O$_7$. Our model describes well the existing experiments and predicts QCP and other high field magnetic properties of these compounds.
A holographic model for antiferromagnetic quantum phase transition induced by magnetic field
Cai, Rong-Gen; Kusmartsev, F V
2015-01-01T23:59:59.000Z
We propose a gravity dual of antiferromagnetic quantum phase transition (QPT) induced by magnetic field and study the criticality in the vicinity of quantum critical point (QCP). Results show the boundary critical theory is a strong coupling theory with dynamic exponent $z=2$. The hyperscaling law is violated and logarithmic corrections appear near the QCP. We compare our theoretical results with experimental data on variety of materials including low-dimensional magnet, BiCoPO$_5$ and pyrochlores, Er$_{2-2x}$Y$_{2x}$Ti$_2$O$_7$. Our model describes well the existing experiments and predicts QCP and other high field magnetic properties of these compounds.
Holographic Fluctuations from Unitary de Sitter Invariant Field Theory
Tom Banks; Willy Fischler; T. J. Torres; Carroll L. Wainwright
2013-06-17T23:59:59.000Z
We continue the study of inflationary fluctuations in Holographic Space Time models of inflation. We argue that the holographic theory of inflation provides a physical context for what is often called dS/CFT. The holographic theory is a quantum theory which, in the limit of a large number of e-foldings, gives rise to a field theory on $S^3$, which is the representation space for a unitary representation of SO(1,4). This is not a conventional CFT, and we do not know the detailed non-perturbative axioms for correlation functions. However, the two- and three-point functions are completely determined by symmetry, and coincide up to a few constants (really functions of the background FRW geometry) with those calculated in a single field slow-roll inflation model. The only significant deviation from slow roll is in the tensor fluctuations. We predict zero tensor tilt and roughly equal weight for all three conformally invariant tensor 3-point functions (unless parity is imposed as a symmetry). We discuss the relation between our results and those of Maldacena, McFadden, Skenderis, and others. Current data can be explained in terms of symmetries and a few general principles, and is consistent with a large class of models, including HST.
Quantum Response at Finite Fields and Breakdown of Chern Numbers
@physics.technion.ac.il #12; Quantum Response at Finite Fields and Breakdown of Chern Numbers 2 On closer inspection oneQuantum Response at Finite Fields and Breakdown of Chern Numbers J E Avron and Z Kons y Department singularity at zero field. We also study the breakdown of Chern numbers associated with the response
String Amplitudes from Moyal String Field Theory
I. Bars; I. Kishimoto; Y. Matsuo
2002-12-29T23:59:59.000Z
We illustrate a basic framework for analytic computations of Feynman graphs using the Moyal star formulation of string field theory. We present efficient methods of computation based on (a) the monoid algebra in noncommutative space and (b) the conventional Feynman rules in Fourier space. The methods apply equally well to perturbative string states or nonperturbative string states involving D-branes. The ghost sector is formulated using Moyal products with fermionic (b,c) ghosts. We also provide a short account on how the purely cubic theory and/or VSFT proposals may receive some clarification of their midpoint structures in our regularized framework.
Quantum Field as a quantum cellular automaton: the Dirac free evolution in one dimension
Alessandro Bisio; Giacomo Mauro D'Ariano; Alessandro Tosini
2015-02-11T23:59:59.000Z
We present a quantum cellular automaton model in one space-dimension which has the Dirac equation as emergent. This model, a discrete-time and causal unitary evolution of a lattice of quantum systems, is derived from the assumptions of homogeneity, parity and time-reversal invariance. The comparison between the automaton and the Dirac evolutions is rigorously set as a discrimination problem between unitary channels. We derive an exact lower bound for the probability of error in the discrimination as an explicit function of the mass, the number and the momentum of the particles, and the duration of the evolution. Computing this bound with experimentally achievable values, we see that in that regime the QCA model cannot be discriminated from the usual Dirac evolution. Finally, we show that the evolution of one-particle states with narrow-band in momentum can be effi- ciently simulated by a dispersive differential equation for any regime. This analysis allows for a comparison with the dynamics of wave-packets as it is described by the usual Dirac equation. This paper is a first step in exploring the idea that quantum field theory could be grounded on a more fundamental quantum cellular automaton model and that physical dynamics could emerge from quantum information processing. In this framework, the discretization is a central ingredient and not only a tool for performing non-perturbative calculation as in lattice gauge theory. The automaton model, endowed with a precise notion of local observables and a full probabilistic interpretation, could lead to a coherent unification of an hypothetical discrete Planck scale with the usual Fermi scale of high-energy physics.
BF-theory in graphene: a route toward topological quantum computing?
Annalisa Marzuoli; Giandomenico Palumbo
2012-06-11T23:59:59.000Z
Besides the plenty of applications of graphene allotropes in condensed matter and nanotechnology, we argue that graphene sheets might be engineered to support room-temperature topological quantum processing of information. The argument is based on the possibility of modeling the monolayer graphene effective action by means of a 3d Topological Quantum Field Theory of BF-type able to sustain non-Abelian anyon dynamics. This feature is the basic requirement of recently proposed theoretical frameworks for fault-tolerant and decoherence protected quantum computation.
Eugene V. Stefanovich
2015-02-16T23:59:59.000Z
This book is an attempt to build a consistent relativistic quantum theory of interacting particles. In the first part of the book "Quantum electrodynamics" we follow rather traditional approach to particle physics. Our discussion proceeds systematically from the principle of relativity and postulates of quantum measurements to the renormalization in quantum electrodynamics. In the second part of the book "Quantum theory of particles" this traditional approach is reexamined. We find that formulas of special relativity should be modified to take into account particle interactions. We also suggest reinterpreting quantum field theory in the language of physical "dressed" particles. This formulation eliminates the need for renormalization and opens up a new way for studying dynamical and bound state properties of quantum interacting systems. The developed theory is applied to realistic physical objects and processes including the energy spectrum of the hydrogen atom, the decay law of moving unstable particles, and the electric field of relativistic electron beams. These results force us to take a fresh look at some core issues of modern particle theories, in particular, the Minkowski space-time unification, the role of quantum fields and renormalization as well as the alleged impossibility of action-at-a-distance. A new perspective on these issues is suggested. It can help to solve the old problem of theoretical physics -- a consistent unification of relativity and quantum mechanics.
The Quantum Theory of Optical Communications
Shapiro, Jeffrey H.
Communication theory applied to lightwave channels is ordinarily carried out using the semiclassical theory of photodetection. Recent development of nonclassical light sources-whose photodetection statistics require the ...
Anomaly constraints and string/F-theory geometry in 6D quantum gravity
Washington Taylor
2010-09-07T23:59:59.000Z
Quantum anomalies, determined by the Atiyah-Singer index theorem, place strong constraints on the space of quantum gravity theories in six dimensions with minimal supersymmetry. The conjecture of "string universality" states that all such theories which do not have anomalies or other quantum inconsistencies are realized in string theory. This paper describes this conjecture and recent work by Kumar, Morrison, and the author towards developing a global picture of the space of consistent 6D supergravities and their realization in string theory via F-theory constructions. We focus on the discrete data for each model associated with the gauge symmetry group and the representation of this group on matter fields. The 6D anomaly structure determines an integral lattice for each gravity theory, which is related to the geometry of an elliptically fibered Calabi-Yau three-fold in an F-theory construction. Possible exceptions to the string universality conjecture suggest novel constraints on low-energy gravity theories which may be identified from the structure of F-theory geometry.
Nuclear effective field theory on the lattice
Hermann Krebs; Bugra Borasoy; Evgeny Epelbaum; Dean Lee; Ulf-G. Meiß ner
2008-10-01T23:59:59.000Z
In the low-energy region far below the chiral symmetry breaking scale (which is of the order of 1 GeV) chiral perturbation theory provides a model-independent approach for quantitative description of nuclear processes. In the two- and more-nucleon sector perturbation theory is applicable only at the level of an effective potential which serves as input in the corresponding dynamical equation. To deal with the resulting many-body problem we put chiral effective field theory (EFT) on the lattice. Here we present the results of our lattice EFT study up to next-to-next-to-leading order in the chiral expansion. Accurate description of two-nucleon phase-shifts and ground state energy ratio of dilute neutron matter up to corrections of higher orders shows that lattice EFT is a promising tool for a quantitative description of low-energy few- and many-body systems.
Closed string field theory in a-gauge
Masako Asano; Mitsuhiro Kato
2012-09-09T23:59:59.000Z
We show that a-gauge, a class of covariant gauges developed for bosonic open string field theory, is consistently applied to the closed string field theory. A covariantly gauge-fixed action of massless fields can be systematically derived from a-gauge-fixed action of string field theory.
Graphene as a Lattice Field Theory
Hands, Simon; Strouthos, Costas
2015-01-01T23:59:59.000Z
We introduce effective field theories for the electronic properties of graphene in terms of relativistic fermions propagating in 2+1 dimensions, and outline how strong inter-electron interactions may be modelled by numerical simulation of a lattice field theory. For strong enough coupling an insulating state can form via condensation of particle-hole pairs, and it is demonstrated that this is a theoretical possibility for monolayer graphene. For bilayer graphene the effect of an interlayer bias voltage can be modelled by the introduction of a chemical potential (akin to isopsin chemical potential in QCD) with no accompanying sign problem; simulations reveal the presence of strong interactions among the residual degrees of freedom at the resulting Fermi surface, which is disrupted by an excitonic condensate. We also present preliminary results for the quasiparticle dispersion, which permit direct estimates of both the Fermi momentum and the induced gap.
Graphene as a Lattice Field Theory
Simon Hands; Wes Armour; Costas Strouthos
2015-01-08T23:59:59.000Z
We introduce effective field theories for the electronic properties of graphene in terms of relativistic fermions propagating in 2+1 dimensions, and outline how strong inter-electron interactions may be modelled by numerical simulation of a lattice field theory. For strong enough coupling an insulating state can form via condensation of particle-hole pairs, and it is demonstrated that this is a theoretical possibility for monolayer graphene. For bilayer graphene the effect of an interlayer bias voltage can be modelled by the introduction of a chemical potential (akin to isopsin chemical potential in QCD) with no accompanying sign problem; simulations reveal the presence of strong interactions among the residual degrees of freedom at the resulting Fermi surface, which is disrupted by an excitonic condensate. We also present preliminary results for the quasiparticle dispersion, which permit direct estimates of both the Fermi momentum and the induced gap.
Magnetic fields and density functional theory
Salsbury Jr., Freddie
1999-02-01T23:59:59.000Z
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
A New Lorentz Violating Nonlocal Field Theory From String-Theory
Ganor, Ori J.
2009-01-01T23:59:59.000Z
hep-th/9908019]. [29] J. Polchinski, “String theory. Vol.2: Superstring theory and beyond,” [30] S. Chakravarty, K.Violating Nonlocal Field Theory From String-Theory Ori J.
The quantum systems control and the optimal control theory
V. F. Krotov
2008-05-22T23:59:59.000Z
Mathematical theory of the quantum systems control is based on some ideas of the optimal control theory. These ideas are developed here as applied to these systems. The results obtained meet the deficiencies in the basis and algorithms of the control synthesis and expand the application of these methods.
Quantum and semiclassical theories of chemical reaction rates
Miller, W.H. [Univ. of California, Berkeley, CA (United States). Dept. of Chemistry]|[Lawrence Berkeley National Lab., CA (United States). Chemical Sciences Div.
1995-09-01T23:59:59.000Z
A rigorous quantum mechanical theory (and a semiclassical approximation thereto) is described for calculating chemical reaction rates ``directly``, i.e., without having to solve the complete state-to-state reactive scattering problem. The approach has many vestiges of transition state theory, for which it may be thought of as the rigorous generalization.
Transition state theory, Siegert eigenstates, and quantum mechanical reaction rates
Miller, William H.
Transition state theory, Siegert eigenstates, and quantum mechanical reaction rates Tamar Seideman variables associated with a transition state (i.e., the saddle point of a potential energy surface), on which a general semiclassical transition state theory is based, are shown to be the semiclassical
From Field Theory to the Hydrodynamics of Relativistic Superfluids
Stetina, Stephan
2015-01-01T23:59:59.000Z
The hydrodynamic description of a superfluid is usually based on a two-fluid picture. In this thesis, basic properties of such a relativistic two-fluid system are derived from the underlying microscopic physics of a complex scalar quantum field theory. To obtain analytic results of all non-dissipative hydrodynamic quantities in terms of field theoretic variables, calculations are first carried out in a low-temperature and weak-coupling approximation. In a second step, the 2-particle-irreducible formalism is applied: This formalism allows for a numerical evaluation of the hydrodynamic parameters for all temperatures below the critical temperature. In addition, a system of two coupled superfluids is studied. As an application, the velocities of first and second sound in the presence of a superflow are calculated. The results show that first (second) sound evolves from a density (temperature) wave at low temperatures to a temperature (density) wave at high temperatures. This role reversal is investigated for ult...
Entropy of quantum channel in the theory of quantum information
Wojciech Roga
2011-10-03T23:59:59.000Z
Quantum channels, also called quantum operations, are linear, trace preserving and completely positive transformations in the space of quantum states. Such operations describe discrete time evolution of an open quantum system interacting with an environment. The thesis contains an analysis of properties of quantum channels and different entropies used to quantify the decoherence introduced into the system by a given operation. Part I of the thesis provides a general introduction to the subject. In Part II, the action of a quantum channel is treated as a process of preparation of a quantum ensemble. The Holevo information associated with this ensemble is shown to be bounded by the entropy exchanged during the preparation process between the initial state and the environment. A relation between the Holevo information and the entropy of an auxiliary matrix consisting of square root fidelities between the elements of the ensemble is proved in some special cases. Weaker bounds on the Holevo information are also established. The entropy of a channel, also called the map entropy, is defined as the entropy of the state corresponding to the channel by the Jamiolkowski isomorphism. In Part III of the thesis, the additivity of the entropy of a channel is proved. The minimal output entropy, which is difficult to compute, is estimated by an entropy of a channel which is much easier to obtain. A class of quantum channels is specified, for which additivity of channel capacity is conjectured. The last part of the thesis contains characterization of Davies channels, which correspond to an interaction of a state with a thermal reservoir in the week coupling limit, under the condition of quantum detailed balance and independence of rotational and dissipative evolutions. The Davies channels are characterized for one-qubit and one-qutrit systems.
Quantum theory of exciton-photon coupling in photonic crystal slabs with embedded quantum wells
D. Gerace; L. C. Andreani
2007-06-04T23:59:59.000Z
A theoretical description of radiation-matter coupling for semiconductor-based photonic crystal slabs is presented, in which quantum wells are embedded within the waveguide core layer. A full quantum theory is developed, by quantizing both the electromagnetic field with a spatial modulation of the refractive index and the exciton center of mass field in a periodic piecewise constant potential. The second-quantized hamiltonian of the interacting system is diagonalized with a generalized Hopfield method, thus yielding the complex dispersion of mixed exciton-photon modes including losses. The occurrence of both weak and strong coupling regimes is studied, and it is concluded that the new eigenstates of the system are described by quasi-particles called photonic crystal polaritons, which can occur in two situations: (i) below the light line, when a resonance between exciton and non-radiative photon levels occurs (guided polaritons), (ii) above the light line, provided the exciton-photon coupling is larger than the intrinsic radiative damping of the resonant photonic mode (radiative polaritons). For a square lattice of air holes, it is found that the energy minimum of the lower polariton branch can occur around normal incidence. The latter result has potential implications for the realization of polariton parametric interactions in photonic crystal slabs.
Scalar field theory on noncommutative Snyder spacetime
Battisti, Marco Valerio [Centre de Physique Theorique, Case 907 Luminy, 13288 Marseille (France); Meljanac, Stjepan [Rudjer Boskovic Institute, Bijenicka c.54, HR-10002 Zagreb (Croatia)
2010-07-15T23:59:59.000Z
We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincare algebra is undeformed. The Lorentz sector is undeformed at both the algebraic and co-algebraic level, but the coproduct for momenta (defining the star product) is non-coassociative. The Snyder-deformed Poincare group is described by a non-coassociative Hopf algebra. The definition of the interacting theory in terms of a nonassociative star product is thus questionable. We avoid the nonassociativity by the use of a space-time picture based on the concept of the realization of a noncommutative geometry. The two main results we obtain are (i) the generic (namely, for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a nonambiguous self-interacting scalar field theory on this space-time. The first-order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.
Theory of Quantum Oscillations in Cuprate Superconductors
Eun, Jonghyoun
2012-01-01T23:59:59.000Z
Cuprate Superconductors . . . . . . . . . . . . . . . . . .J. Schried?er. Theory of superconductivity. Phys. Rev. , [Tinkham. Introduction to Superconductivity. Dover, New York,
Lie-Algebroid Formulation of k-Cosymplectic Field Theories
Roman-Roy, Narciso [Departamento de Matematica Aplicada IV. Edificio C-3, Campus Norte UPC. C/Jordi Girona 1. 08034 Barcelona (Spain); Salgado, Modesto; Vilarino, Silvia [Departamento de Xeometria e Topoloxia. Facultade de Matematicas, Universidade de Santiago de Compostela. 15782 Santiago de Compostela (Spain)
2009-05-06T23:59:59.000Z
We present a description for the k-cosymplectic formalism of Hamiltonian field theories in terms of Lie algebroids.
Extention cohomological fields theories and noncommutative Frobenius manifolds
S. M. Natanzon
2005-10-04T23:59:59.000Z
We construct some extension ({\\it Stable Field Theory}) of Cohomological Field Theory. The Stable Field Theory is a system of homomorphisms to some vector spaces generated by spheres and disks with punctures. It is described by a formal tensor series, satisfying to some system of "differential equations". In points of convergence the tensor series generate special noncommutative analogues of Frobenius algebras, describing 'Open-Closed' Topological Field Theories.
Systems of two heavy quarks with effective field theories
Nora Brambilla
2006-09-22T23:59:59.000Z
I discuss results and applications of QCD nonrelativistic effective field theories for systems with two heavy quarks.
From Field Theory to the Hydrodynamics of Relativistic Superfluids
Stephan Stetina
2015-01-31T23:59:59.000Z
The hydrodynamic description of a superfluid is usually based on a two-fluid picture. In this thesis, basic properties of such a relativistic two-fluid system are derived from the underlying microscopic physics of a complex scalar quantum field theory. To obtain analytic results of all non-dissipative hydrodynamic quantities in terms of field theoretic variables, calculations are first carried out in a low-temperature and weak-coupling approximation. In a second step, the 2-particle-irreducible formalism is applied: This formalism allows for a numerical evaluation of the hydrodynamic parameters for all temperatures below the critical temperature. In addition, a system of two coupled superfluids is studied. As an application, the velocities of first and second sound in the presence of a superflow are calculated. The results show that first (second) sound evolves from a density (temperature) wave at low temperatures to a temperature (density) wave at high temperatures. This role reversal is investigated for ultra-relativistic and near-nonrelativistic systems for zero and nonzero superflow. The studies carried out in this thesis are of a very general nature as one does not have to specify the system for which the microscopic field theory is an effective description. As a particular example, superfluidity in dense quark and nuclear matter in compact stars are discussed.
On quantum theories of the mind
Henry P. Stapp
1997-11-26T23:59:59.000Z
Replies are given to arguments advanced in this journal that claim to show that it is to nonlinear classical mechanics rather than quantum mechanics that one must look for the physical underpinnings of consciousness.
Working Group Report: Lattice Field Theory
Blum, T.; et al.,
2013-10-22T23:59:59.000Z
This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
Lattice field theory simulations of graphene
Joaquín E. Drut; Timo A. Lähde
2009-04-21T23:59:59.000Z
We discuss the Monte Carlo method of simulating lattice field theories as a means of studying the low-energy effective theory of graphene. We also report on simulational results obtained using the Metropolis and Hybrid Monte Carlo methods for the chiral condensate, which is the order parameter for the semimetal-insulator transition in graphene, induced by the Coulomb interaction between the massless electronic quasiparticles. The critical coupling and the associated exponents of this transition are determined by means of the logarithmic derivative of the chiral condensate and an equation-of-state analysis. A thorough discussion of finite-size effects is given, along with several tests of our calculational framework. These results strengthen the case for an insulating phase in suspended graphene, and indicate that the semimetal-insulator transition is likely to be of second order, though exhibiting neither classical critical exponents, nor the predicted phenomenon of Miransky scaling.
Goddard III, William A.
Quantum mechanics based force field for carbon ,,QMFF-Cx... validated to reproduce the mechanical mechanics based force field for carbon QMFF-Cx by fitting to results from density functional theory . A third, eclipsed geometry is calculated to be much higher in energy. The QMFF-Cx force field leads
Transfer operators and topological field theory
Igor V. Ovchinnikov
2014-10-24T23:59:59.000Z
The transfer operator (TO) formalism of the dynamical systems (DS) theory is reformulated here in terms of the recently proposed cohomological theory (ChT) of stochastic differential equations (SDE). It turns out that the stochastically generalized TO (GTO) of the DS theory is the finite-time ChT Fokker-Planck evolution operator. As a result comes the supersymmetric trivialization of the so-called sharp trace and sharp determinant of the GTO, with the former being the Witten index of the ChT. Moreover, the Witten index is also the stochastic generalization of the Lefschetz index so that it equals the Euler characteristic of the (closed) phase space for any flow vector field, noise metric, and temperature. The enabled possibility to apply the spectral theorems of the DS theory to the ChT Fokker-Planck operators allows to extend the previous picture of the spontaneous topological supersymmetry (Q-symmetry) breaking onto the situations with negative ground state's attenuation rate. The later signifies the exponential growth of the number of periodic solutions/orbits in the large time limit, which is the unique feature of chaotic behavior proving that the spontaneous breakdown of Q-symmetry is indeed the field-theoretic definition and stochastic generalization of the concept of deterministic chaos. In addition, the previously proposed low-temperature classification of SDE's, i.e., thermodynamic equilibrium / noise-induced chaos ((anti-)instanton condensation) / ordinary chaos (non-integrability), is complemented by the discussion of the high-temperature regime where the sharp boundary between the noise-induced and ordinary chaotic phases must smear out into a crossover, and at even higher temperatures the Q-symmetry is restored. An unambiguous resolution of the Ito-Stratonovich dilemma in favor of the Stratonovich approach and/or Weyl quantization is also presented.
Quantum theory as a critical regime of language dynamics
Alexei Grinbaum
2015-01-12T23:59:59.000Z
Quantum mechanics relies on the cut between the observer and the quantum system, but it does not define the observer physically. We propose an informational definition based on bounded complexity of strings. Language dynamics then leads to an emergent continuous model in the critical regime. Restricting it to a subfamily of `quantum' binary codes describing `bipartite systems', we find strong evidence of an upper bound on bipartite correlations equal to 2.82537. This is measurably different from the Tsirelson bound of the CHSH inequality. If such a reconstruction of quantum theory is experimentally confirmed, it would show that the Hilbert space formalism is but an effective description of a fundamental `linguistic' theory in the critical regime.
Perturbative diagrams in string field theory
Washington Taylor
2002-07-13T23:59:59.000Z
A general algorithm is presented which gives a closed-form expression for an arbitrary perturbative diagram of cubic string field theory at any loop order. For any diagram, the resulting expression is given by an integral of a function of several infinite matrices, each built from a finite number of blocks containing the Neumann coefficients of Witten's 3-string vertex. The closed-form expression for any diagram can be approximated by level truncation on oscillator level, giving a computation involving finite size matrices. Some simple tree and loop diagrams are worked out as examples of this approach.
Perturbative computations in string field theory
Washington Taylor
2004-04-15T23:59:59.000Z
These notes describe how perturbative on-shell and off-shell string amplitudes can be computed using string field theory. Computational methods for approximating arbitrary amplitudes are discussed, and compared with standard world-sheet methods for computing on-shell amplitudes. These lecture notes are not self-contained; they contain the material from W. Taylor's TASI 2003 lectures not covered in the recently published ``TASI 2001'' notes {\\tt hep-th/0311017} by Taylor and Zwiebach, and should be read as a supplement to those notes.
Thermalization of Strongly Coupled Field Theories
Balasubramanian, V. [David Rittenhouse Laboratory, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States); Bernamonti, A.; Copland, N.; Craps, B.; Staessens, W. [Theoretische Natuurkunde, Vrije Universiteit Brussel, and International Solvay Institutes, B-1050 Brussels (Belgium); Boer, J. de [Institute for Theoretical Physics, University of Amsterdam, 1090 GL Amsterdam (Netherlands); Keski-Vakkuri, E. [Helsinki Institute of Physics and Department of Physics, FIN-00014 University of Helsinki (Finland); Mueller, B. [Department of Physics and CTMS, Duke University, Durham, North Carolina 27708 (United States); Schaefer, A. [Institut fuer Theoretische Physik, Universitaet Regensburg, D-93040 Regensburg (Germany); Shigemori, M. [Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan)
2011-05-13T23:59:59.000Z
Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in d=2, 3, and 4 to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest and sets a time scale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volume-independent for small volumes but slows for larger volumes. In this setting, the UV thermalizes first.
Drift estimation from a simple field theory
Mendes, F. M.; Figueiredo, A. [Instituto de Fisica, Universidade de Brasilia, CP: 04455, 70919-970-Brasilia (Brazil)
2008-11-06T23:59:59.000Z
Given the outcome of a Wiener process, what can be said about the drift and diffusion coefficients? If the process is stationary, these coefficients are related to the mean and variance of the position displacements distribution. However, if either drift or diffusion are time-dependent, very little can be said unless some assumption about that dependency is made. In Bayesian statistics, this should be translated into some specific prior probability. We use Bayes rule to estimate these coefficients from a single trajectory. This defines a simple, and analytically tractable, field theory.
Toolbox for reconstructing quantum theory from rules on information acquisition
Hoehn, Philipp A
2015-01-01T23:59:59.000Z
We develop a novel operational approach for reconstructing (qubit) quantum theory from elementary rules on information acquisition. The focus lies on an observer O interrogating a system S with binary questions and S's state is taken as O's `catalogue of knowledge' about S. The mathematical tools of the framework are simple and we attempt to highlight all underlying assumptions to provide a handle for future generalizations. Five principles are imposed, asserting (1) a limit on the amount of information available to O; (2) the mere existence of complementary information; (3) the possibility for O's information to be `in superposition'; (4) O's information to be preserved in between interrogations; and, (5) continuity of time evolution. This approach permits a constructive derivation of quantum theory, elucidating how the ensuing independence, complementarity and compatibility structure of O's questions matches that of projective measurements in quantum theory, how entanglement and monogamy of entanglement and...
Invariant Set Theory and the Symbolism of Quantum Measurement
T. N. Palmer
2015-02-24T23:59:59.000Z
Elements of a novel theory of quantum physics are developed, synthesising the role of symbolism in describing quantum measurement and in the topological representation of fractal invariant sets in nonlinear dynamical systems theory. In this synthesis, the universe $U$ is treated as an isolated deterministic dynamical system evolving precisely on a measure-zero fractal invariant subset $I_U$ of its state space. A non-classical approach to the physics of $U$ is developed by treating the geometry of $I_U$ as more primitive than dynamical evolution equations on $I_U$. A specific symbolic representation of $I_U$ is constructed which encodes quaternionic multiplication and from which the statistical properties of complex Hilbert Space vectors are emergent. The Hilbert Space itself arises as the singular limit of Invariant Set Theory as a fractal parameter $N \\rightarrow \\infty$. Although the Hilbert Space of quantum theory is counterfactually complete, the measure-zero set $I_U$ is counterfactually incomplete, no matter how large is $N$. Such incompleteness allows reinterpretations of familiar quantum phenomena, consistent with realism and local causality. The non-computable nature of $I_U$ ensures that these reinterpretations are neither conspiratorial nor retrocausal and, through a homeomorphism with the ring of $2^N$-adic integers, are robust to noise and hence not fine tuned. The non-commutativity of Hilbert Space observables emerges from the symbolic representation of $I_U$ through the generic number-theoretic incommensurateness of $\\phi/\\pi$ and $\\cos \\phi$. Invariant Set Theory implies a much stronger synergy between cosmology and quantum physics than exists in contemporary theory, suggesting a novel approach to synthesising gravitational and quantum physics and providing new perspectives on the dark universe and information loss in black holes.
Towards a K-theory description of quantum hair
Garcia-Compean, H.; Loaiza-Brito, O. [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del I.P.N., P.O. Box 14-740, 07000, Mexico D.F (Mexico); Departamento de Fisica, Universidad de Guanajuato, C.P. 37150, Leon, Guanajuato (Mexico)
2012-08-24T23:59:59.000Z
The first steps towards a proposal for a description of the quantum hair in 4D supersymmetric black holes in string Calabi-Yau (CY) compactifications are given. The quantum hair consisting of electric and magnetic fractional charges in black holes are derived from periods of the CY's torsion cycles. In the process a K-theory interpretation of the quantum hair in terms of the Atiyah-Hirzebruch spectral sequence is carried out. Finally, the same procedure is considered for torsion cycles of certain generalized CY's threefolds such as half-flat manifolds.
Four-dimensional deformed special relativity from group field theories
Girelli, Florian [SISSA, Via Beirut 2-4, 34014 Trieste, Italy and INFN, Sezione di Trieste (Italy); School of Physics, University of Sydney, Sydney, New South Wales 2006 (Australia); Livine, Etera R. [Laboratoire de Physique, ENS Lyon, CNRS UMR 5672, 46 Allee d'Italie, 69007 Lyon (France); Oriti, Daniele [Perimeter Institute for Theoretical Physics, 31 Caroline St, Waterloo, Ontario N2L 2Y5 (Canada); Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, Utrecht 3584 TD (Netherlands); Albert Einstein Institute, Am Muehlenberg 4, Golm (Germany)
2010-01-15T23:59:59.000Z
We derive a scalar field theory of the deformed special relativity type, living on noncommutative {kappa}-Minkowski space-time and with a {kappa}-deformed Poincare symmetry, from the SO(4,1) group field theory defining the transition amplitudes for topological BF theory in 4 space-time dimensions. This is done at a nonperturbative level of the spin foam formalism working directly with the group field theory (GFT). We show that matter fields emerge from the fundamental model as perturbations around a specific phase of the GFT, corresponding to a solution of the fundamental equations of motion, and that the noncommutative field theory governs their effective dynamics.
Theory of an optomechanical quantum heat engine
Keye Zhang; Francesco Bariani; Pierre Meystre
2014-08-13T23:59:59.000Z
Coherent interconversion between optical and mechanical excitations in an optomechanical cavity can be used to engineer a quantum heat engine. This heat engine is based on an Otto cycle between a cold photonic reservoir and a hot phononic reservoir [Phys. Rev. Lett. 112, 150602 (2014)]. Building on our previous work, we (i) develop a detailed theoretical analysis of the work and the efficiency of the engine, and (ii) perform an investigation of the quantum thermodynamics underlying this scheme. In particular, we analyze the thermodynamic performance in both the dressed polariton picture and the original bare photon and phonon picture. Finally, (iii) a numerical simulation is performed to derive the full evolution of the quantum optomechanical system during the Otto cycle, by taking into account all relevant sources of noise.
Finite temperature field theory on the Moyal plane
Akofor, E. [Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (United States); Balachandran, A. P. [Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (United States); Departmento de Matematicas, Universedad Carlos III de Madrid, 28911 Leganes, Madrid (Spain)
2009-08-01T23:59:59.000Z
In this paper, we initiate the study of finite temperature quantum field theories on the Moyal plane. Such theories violate causality which influences the properties of these theories. In particular, causality influences the fluctuation-dissipation theorem: as we show, a disturbance in a space-time region M{sub 1} creates a response in a space-time region M{sub 2} spacelike with respect to M{sub 1} (M{sub 1}xM{sub 2}). The relativistic Kubo formula with and without noncommutativity is discussed in detail, and the modified properties of relaxation time and the dependence of mean square fluctuations on time are derived. In particular, the Sinha-Sorkin result [Phys. Rev. B 45, 8123 (1992)] on the logarithmic time dependence of the mean square fluctuations is discussed in our context. We derive an exact formula for the noncommutative susceptibility in terms of the susceptibility for the corresponding commutative case. It shows that noncommutative corrections in the four-momentum space have remarkable periodicity properties as a function of the four-momentum k. They have direction dependence as well and vanish for certain directions of the spatial momentum. These are striking observable signals for noncommutativity. The Lehmann representation is also generalized to any value of the noncommutativity parameter {theta}{sup {mu}}{sup {nu}} and finite temperatures.
Anomalous critical fields in quantum critical superconductors
Putzke, C.; Walmsley, P.; Fletcher, J.D.; Malone, L.; Vignolles, D.; Proust, C.; Badoux, S.; See, P.; Beere, H.E.; Ritchie, D.A.; Kasahara, S.; Mizukami, Y.; Shibauchi, T.; Matsuda, Y.; Carrington, A.
2015-01-01T23:59:59.000Z
-temperature superconductivity. However, the exact mechanism by which this occurs remains poorly understood. The iron-pnictide superconductor BaFe2(As1?xPx)2 is perhaps the clearest example to date of a high temperature quantum critical superconductor, and so it is a... mixing of antiferromagnetism and superconductivity, suggesting that a highly unusual vortex state is realised in quantum critical superconductors. Quantum critical points (QCPs) can be associated with a variety of different order-disorder phenomena...
Quantum critical benchmark for density functional theory
Paul E. Grabowski; Kieron Burke
2014-08-09T23:59:59.000Z
Two electrons at the threshold of ionization represent a severe test case for electronic structure theory. A pseudospectral method yields a very accurate density of the two-electron ion with nuclear charge close to the critical value. Highly accurate energy components and potentials of Kohn-Sham density functional theory are given, as well as a useful parametrization of the critical density. The challenges for density functional approximations and the strength of correlation are also discussed.
Vacuum energy momentum tensor in (2+1) NC scalar field theory
P. Nicolini
2004-01-27T23:59:59.000Z
A scalar field in (2+1) dimensional Minkowski space-time is considered. Postulating noncommutative spatial coordinates, one is able to determine the (UV finite) vacuum expectation value of the quantum field energy momentum tensor. Calculation for the (3+1) case has been performed considering only two noncommutative coordinates. The results lead to a vacuum energy with a lowered degree of divergence, with respect to that of ordinary commutative theory.
Noncommutative field theories: The noncommutative Chern-Simons model
Gomes, M.; Silva, A. J. da [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo (Brazil)
2006-11-03T23:59:59.000Z
We present some results on the ultraviolet/infrared mixing for canonical field theory in three and four space-time dimensions. Special emphasis is given to the analysis of theories containing the Chern-Simons field and it is argued that for supersymmetric models the effect of the mixing is in general mild leading to consistent theories as far as renormalization is concerned.
Quantum-mechanical theory of optomechanical Brillouin cooling
Tomes, Matthew; Bahl, Gaurav; Carmon, Tal [Department of Electrical Engineering, University of Michigan, Ann Arbor, Michigan 48109 (United States); Marquardt, Florian [Institut fuer Theoretische Physik, Universitaet Erlangen-Nuernberg, Staudtstrasse 7, D-91058 Erlangen (Germany); Max Planck Institute for the Science of Light, Guenther-Scharowsky-Strasse 1/Bau 24, D-91058 Erlangen (Germany)
2011-12-15T23:59:59.000Z
We analyze how to exploit Brillouin scattering of light from sound for the purpose of cooling optomechanical devices and present a quantum-mechanical theory for Brillouin cooling. Our analysis shows that significant cooling ratios can be obtained with standard experimental parameters. A further improvement of cooling efficiency is possible by increasing the dissipation of the optical anti-Stokes resonance.
Simplification of additivity conjecture in quantum information theory
Motohisa Fukuda
2007-04-09T23:59:59.000Z
We simplify some conjectures in quantum information theory; the additivity of minimal output entropy, the multiplicativity of maximal output p-norm and the superadditivity of convex closure of output entropy. We construct a unital channel for a given channel so that they share the above additivity properties; we can reduce the conjectures for all channels to those for unital channels.
Toolbox for reconstructing quantum theory from rules on information acquisition
Philipp A Hoehn
2014-12-29T23:59:59.000Z
We develop a novel operational approach for reconstructing (qubit) quantum theory from elementary rules on information acquisition. The focus lies on an observer O interrogating a system S with binary questions and S's state is taken as O's `catalogue of knowledge' about S. The mathematical tools of the framework are simple and we attempt to highlight all underlying assumptions to provide a handle for future generalizations. Five principles are imposed, asserting (1) a limit on the amount of information available to O; (2) the mere existence of complementary information; (3) the possibility for O's information to be `in superposition'; (4) O's information to be preserved in between interrogations; and, (5) continuity of time evolution. This approach permits a constructive derivation of quantum theory, elucidating how the ensuing independence, complementarity and compatibility structure of O's questions matches that of projective measurements in quantum theory, how entanglement and monogamy of entanglement and, more generally, how the correlation structure of arbitrarily many qubits and rebits arises. The principles yield a reversible time evolution and a quadratic measure, quantifying O's information about S. Finally, it is shown that the five principles admit two solutions for the simplest case of a single elementary system: the Bloch ball and disc as state spaces for a qubit and rebit, respectively, together with their symmetries as time evolution groups. The reconstruction is completed in a companion paper where an additional postulate eliminates the rebit case. This approach is conceptually close to the relational interpretation of quantum theory.
Wilsonian Renormalization of Noncommutative Scalar Field Theory
Razvan Gurau; Oliver J. Rosten
2009-07-22T23:59:59.000Z
Drawing on analogies with the commutative case, the Wilsonian picture of renormalization is developed for noncommutative scalar field theory. The dimensionful noncommutativity parameter, theta, induces several new features. Fixed-points are replaced by `floating-points' (actions which are scale independent only up to appearances of theta written in cutoff units). Furthermore, it is found that one must use correctly normalized operators, with respect to a new scalar product, to define the right notion of relevance and irrelevance. In this framework it is straightforward and intuitive to reproduce the classification of operators found by Grosse & Wulkenhaar, around the Gaussian floating-point. The one-loop beta-function of their model is computed directly within the exact renormalization group, reproducing the previous result that it vanishes in the self-dual theory, in the limit of large cutoff. With the link between this methodology and earlier results made, it is discussed how the vanishing of the beta-function to all loops, as found by Disertori et al., should be interpreted in a Wilsonian framework.
Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories
Chong-Sun Chu; Jerzy Lukierski; Wojtek J. Zakrzewski
2002-01-31T23:59:59.000Z
The IR/UV mixing and the violation of unitarity are two of the most intriguing aspects of noncommutative quantum field theories. In this paper the relation between these two phenomena is explained and established. We start out by showing that the S-matrix of noncommutative field theories is hermitian analytic. As a consequence, a noncommutative field theory is unitary if the discontinuities of its Feynman diagram amplitudes agree with the expressions calculated using the Cutkosky formulae. These unitarity constraints relate the discontinuities of amplitudes with physical intermediate states; and allow us to see how the IR/UV mixing may lead to a breakdown of unitarity. Specifically, we show that the IR/UV singularity does not lead to the violation of unitarity in the space-space noncommutative case, but it does lead to its violation in a space-time noncommutative field theory. As a corollary, noncommutative field theory without IR/UV mixing will be unitary in both the space-space and space-time noncommutative case. To illustrate this, we introduce and analyse the noncommutative Lee model--an exactly solvable quantum field theory. We show that the model is free from the IR/UV mixing in both the space-space and space-time noncommutative cases. Our analysis is exact. Due to absence of the IR/UV mixing one can expect that the theory is unitary. We present some checks supporting this claim. Our analysis provides a counter example to the generally held beliefs that field theories with space-time noncommutativity are non-unitary.
Foundations for proper-time relativistic quantum theory
Tepper L. Gill; Trey Morris; Stewart K. Kurtz
2015-03-06T23:59:59.000Z
This paper is a progress report on the foundations for the canonical proper-time approach to relativistic quantum theory. We first review the the standard square-root equation of relativistic quantum theory, followed by a review of the Dirac equation, providing new insights into the physical properties of both. We then introduce the canonical proper-time theory. For completeness, we give a brief outline of the canonical proper-time approach to electrodynamics and mechanics, and then introduce the canonical proper-time approach to relativistic quantum theory. This theory leads to three new relativistic wave equations. In each case, the canonical generator of proper-time translations is strictly positive definite, so that it represents a particle. We show that the canonical proper-time extension of the Dirac equation for Hydrogen gives results that are consistently closer to the experimental data, when compared to the Dirac equation. However, these results are not sufficient to account for either the Lamb shift or the anomalous magnetic moment.
Twist Field as Three String Interaction Vertex in Light Cone String Field Theory
Isao Kishimoto; Sanefumi Moriyama; Shunsuke Teraguchi
2007-03-22T23:59:59.000Z
It has been suggested that matrix string theory and light-cone string field theory are closely related. In this paper, we investigate the relation between the twist field, which represents string interactions in matrix string theory, and the three-string interaction vertex in light-cone string field theory carefully. We find that the three-string interaction vertex can reproduce some of the most important OPEs satisfied by the twist field.
Tachyonic Field Theory and Neutrino Mass Running
U. D. Jentschura
2012-05-01T23:59:59.000Z
In this paper three things are done. (i) We investigate the analogues of Cerenkov radiation for the decay of a superluminal neutrino and calculate the Cerenkov angles for the emission of a photon through a W loop, and for a collinear electron-positron pair, assuming the tachyonic dispersion relation for the superluminal neutrino. The decay rate of a freely propagating neutrino is found to depend on the shape of the assumed dispersion relation, and is found to decrease with decreasing tachyonic mass of the neutrino. (ii) We discuss a few properties of the tachyonic Dirac equation (symmetries and plane-wave solutions), which may be relevant for the description of superluminal neutrinos seen by the OPERA experiment, and discuss the calculation of the tachyonic propagator. (iii) In the absence of a commonly accepted tachyonic field theory, and in view of an apparent "running" of the observed neutrino mass with the energy, we write down a model Lagrangian, which describes a Yukawa-type interaction of a neutrino coupling to a scalar background field via a scalar-minus-pseudoscalar interaction. This constitutes an extension of the standard model. If the interaction is strong, then it leads to a substantial renormalization-group "running" of the neutrino mass and could potentially explain the experimental observations.
Quantum Field Effects in Stationary Electron Spin Resonance Spectroscopy
Dmitri Yerchuck; Vyacheslav Stelmakh; Yauhen Yerchak; Alla Dovlatova
2015-01-28T23:59:59.000Z
It is proved on the example of electron spin resonance (ESR) studies of anthracites, that by strong electron-photon and electron-phonon interactions the formation of the coherent system of the resonance phonons takes place. The acoustic quantum Rabi oscillations were observed for the first time in ESR-spectroscopy. Its Rabi frequency value on the first damping stage was found to be equal 920.6 kHz, being to be independent on the microwave power level in the range 20 - 6 dB [0 dB corresponds to 100 mW]. By the subsequent increase of the microwave power the stepwise transition to the phenomenon of nonlinear quantum Rabi oscillations, characterised by splitting of the oscillation group of lines into two subgroups with doubling of the total lines' number takes place. Linewidth of an individual oscillation line becomes approximately the twofold narrower, being to be equal the only to $0.004 \\pm 0.001$ G. Along with the absorption process of EM-field energy the emission process was observed. It was found, that the emission process is the realization of the acoustic spin resonance, the source of acoustic wave power in which is the system of resonance phonons, accumulated in the samples by the registration with AFC. It has been found, that the lifetime of coherent state of a collective subsystem of resonance phonons in anthracites is very long and even by room temperature it is evaluated by the value exceeding 4.6 minutes. The model of new kinds of instantons was proposed. They are considered to be similar in the mathematical structure to Su-Schrieffer-Heeger solitons with "propagation" direction along time $t$-axis instead of space $z$-axis. The proof, that the superconductivity state in the anthracite samples studied is produced at the room temperature in ESR conditions in the accordance with the theory of the quantised acoustic field, has experimentally been obtained.
Open quantum systems and random matrix theory
Mulhall, Declan [Department of Physics/Engineering, University of Scranton, Scranton, Pennsylvania 18510-4642 (United States)
2014-10-15T23:59:59.000Z
A simple model for open quantum systems is analyzed with RMT. The system is coupled to the continuum in a minimal way. In this paper we see the effect of opening the system on the level statistics, in particular the level spacing, width distribution and ?{sub 3}(L) statistic are examined as a function of the strength of this coupling. The usual super-radiant state is observed, and it is seen that as it is formed, the level spacing and ?{sub 3}(L) statistic exhibit the signatures of missed levels.
Yuya Sasai; Naoki Sasakura
2009-05-13T23:59:59.000Z
We investigate the unitarity of three dimensional noncommutative scalar field theory in the Lie algebraic noncommutative spacetime [x^i,x^j]=2i kappa epsilon^{ijk}x_k. This noncommutative field theory possesses a SL(2,R)/Z_2 group momentum space, which leads to a Hopf algebraic translational symmetry. We check the Cutkosky rule of the one-loop self-energy diagrams in the noncommutative phi^3 theory when we include a braiding, which is necessary for the noncommutative field theory to possess the Hopf algebraic translational symmetry at quantum level. Then, we find that the Cutkosky rule is satisfied if the mass is less than 1/(2^(1/2)kappa).
Coulomb-corrected quantum trajectories in strong-field ionization RID A-7617-2010 RID A-5158-2009
Popruzhenko, S. V.; Paulus, Gerhard G.; Bauer, D.
2008-01-01T23:59:59.000Z
dominated by the laser field. In this work we introduce a Coulomb-corrected strong-field theory of photoionization based on quantum trajectories and show how binding forces lead to strong qualitative effects in above-threshold ionization of atoms. We examine...
Seeking the balance: Patching double and exceptional field theories
G. Papadopoulos
2014-09-29T23:59:59.000Z
We investigate the patching of double and exceptional field theories. In double field theory the patching conditions imposed on the spacetime after solving the strong section condition imply that the 3-form field strength $H$ is exact. A similar conclusion can be reached for the form field strengths of exceptional field theories after some plausive assumptions are made on the relation between the transition functions of the additional coordinates and the patching data of the form field strengths. We illustrate the issues that arise, and explore several alternative options which include the introduction of C-folds and of the topological geometrisation condition.
Tom Banks; Willy Fischler
2013-01-24T23:59:59.000Z
We present a theory of accelerated observers in the formalism of holographic space time, and show how to define the analog of the Unruh effect for a one parameter set of accelerated observers in a causal diamond in Minkowski space. The key fact is that the formalism splits the degrees of freedom in a large causal diamond into particles and excitations on the horizon. The latter form a large heat bath for the particles, and different Hamiltonians, describing a one parameter family of accelerated trajectories, have different couplings to the bath. We argue that for a large but finite causal diamond the Hamiltonian describing a geodesic observer has a residual coupling to the bath and that the effect of the bath is finite over the long time interval in the diamond. We find general forms of the Hamiltonian, which guarantee that the horizon degrees of freedom will decouple in the limit of large diamonds, leaving over a unitary evolution operator for particles, with an asymptotically conserved energy. That operator converges to the S-matrix in the infinite diamond limit. The S-matrix thus arises from integrating out the horizon degrees of freedom, in a manner reminiscent of, but distinct from, Matrix Theory. We note that this model for the S-matrix implies that Quantum Gravity, as opposed to quantum field theory, has a natural adiabatic switching off of the interactions. We argue that imposing Lorentz invariance on the S-matrix is natural, and guarantees super-Poincare invariance in the HST formalism. Spatial translation invariance is seen to be the residuum of the consistency conditions of HST.
TASI Lectures on Holographic Space-Time, SUSY and Gravitational Effective Field Theory
Tom Banks
2010-09-23T23:59:59.000Z
I argue that the conventional field theoretic notion of vacuum state is not valid in quantum gravity. The arguments use gravitational effective field theory, as well as results from string theory, particularly the AdS/CFT correspondence. Different solutions of the same low energy gravitational field equations correspond to different quantum systems, rather than different states in the same system. I then introduce {\\it holographic space-time} a quasi-local quantum mechanical construction based on the holographic principle. I argue that models of quantum gravity in asymptotically flat space-time will be exactly super-Poincare invariant, because the natural variables of holographic space-time for such a system, are the degrees of freedom of massless superparticles. The formalism leads to a non-singular quantum Big Bang cosmology, in which the asymptotic future is required to be a de Sitter space, with cosmological constant (c.c.) determined by cosmological initial conditions. It is also approximately SUSic in the future, with the gravitino mass $K \\Lambda^{1/4}$.
Mirror-induced decoherence in hybrid quantum-classical theory
Aniello Lampo; Lorenzo Fratino; Hans-Thomas Elze
2014-10-16T23:59:59.000Z
We re-analyse the optomechanical interferometer experiment proposed by Marshall, Simon, Penrose and Bouwmeester with the help of a recently developed quantum-classical hybrid theory. This leads to an alternative evaluation of the mirror induced decoherence. Surprisingly, we find that it behaves essentially in the same way for suitable initial conditions and experimentally relevant parameters, no matter whether the mirror is considered a classical or quantum mechanical object. We discuss the parameter ranges where this result holds and possible implications for a test of spontaneous collapse models, for which this experiment has been designed.
Irreducibility of the set of field operators in NC QFT
Mnatsakanova, M. N., E-mail: mnatsak@theory.sinp.msu.ru [Lomonosov Moscow State University, Skobeltsyn Institute of Nuclear Physics (Russian Federation); Vernov, Yu. S. [Russian Academy of Sciences, Institute for Nuclear Research (Russian Federation)] [Russian Academy of Sciences, Institute for Nuclear Research (Russian Federation)
2013-10-15T23:59:59.000Z
Irreducibility of the set of quantum field operators has been proved in noncommutative quantum field theory in the general case when time does not commute with spatial variables.
The spacetime of double field theory: Review, remarks, and outlook
Hohm, Olaf
We review double field theory (DFT) with emphasis on the doubled spacetime and its generalized coordinate transformations, which unify diffeomorphisms and b-field gauge transformations. We illustrate how the composition ...
Modal field theory and quasi-sparse eigenvector diagonalization
Dean Lee
2000-04-01T23:59:59.000Z
We review recent developments in non-perturbative field theory using modal field methods. We discuss Monte Carlo results as well as a new diagonalization technique known as the quasi-sparse eigenvector method.
Consistent Kaluza-Klein truncations via exceptional field theory
Hohm, Olaf
We present the generalized Scherk-Schwarz reduction ansatz for the full supersymmetric exceptional field theory in terms of group valued twist matrices subject to consistency equations. With this ansatz the field equations ...
The gauge algebra of double field theory and Courant brackets
Hull, Chris
We investigate the symmetry algebra of the recently proposed field theory on a doubled torus that describes closed string modes on a torus with both momentum and winding. The gauge parameters are constrained fields on the ...
From Quantum Mechanics to String Theory
's Constant Newton's constant G appears in the universal law of gravitation: It determines the strength potential energy that we see as mass a spontaneously broken symmetry is a symmetry of the laws of nature. An object of mass m in a gravitational field g feels a force of F = mg This is similar to electromagnetism
Magnetic fields and density functional theory
Jr, F.-Salsbury
2010-01-01T23:59:59.000Z
development of the general theory, Grayce and Harris used an electron gas approach to obtain a local energy
Benjamin Chih-Chien Nien
2006-10-11T23:59:59.000Z
This paper attempts to analyze central place theory of spatial economics based on supply and demand theory in microeconomics and field theory in physics, and also discuss their relationship. Three most important research findings are described below. Firstly, the concept of market equilibrium could be expressed in the mathematical form of physics field theory under proper hypothesis. That is because the most important aspect of field theory model is that complex analysis is taken as a key mathematical tool. If assuming that imaginary part is neglected in this model, it is found that this model has the same mathematical structure as supply and demand theory of microeconomics. Secondly, the mathematical model of field theory can be applied to express clearly many concepts of central place theory, or even introduce many new concepts. Thirdly, it could also be taken as a study of combining the Hotelling Model and Moses Model for the location theory in another mathematic approach.
M-Theory Brane as Giant Graviton and the Fractional Quantum Hall Effect
Ran Huo
2006-07-30T23:59:59.000Z
A small number of M-theory branes as giant gravitons in the M-theory sector of LLM geometry is studied as a probe. The abelian way shows that the low energy effective action for M-theory brane is exactly the 2d electron subject to a vertical magnetic field. We also briefly discuss the microscopic description of M2-brane giant graviton in this geometry, in the language of a combination of D0-branes as fuzzy 2-spheres. Then we go to the well-established Noncommutative Chern-Simons theory description. After quantization, well behaved Fractional Quantum Hall Effect is demonstrated. This goes beyond the original LLM description and should be some indication of novel geometry.
Categorical Operator Algebraic Foundations of Relational Quantum Theory
Paolo Bertozzini
2014-12-23T23:59:59.000Z
We provide an algebraic formulation of C.Rovelli's relational quantum theory that is based on suitable notions of "non-commutative" higher operator categories, originally developed in the study of categorical non-commutative geometry. As a way to implement C.Rovelli's original intuition on the relational origin of space-time, in the context of our proposed algebraic approach to quantum gravity via Tomita-Takesaki modular theory, we tentatively suggest to use this categorical formalism in order to spectrally reconstruct non-commutative relational space-time geometries from categories of correlation bimodules between operator algebras of observables. Parts of this work are joint collaborations with: Dr.Roberto Conti (Sapienza Universita' di Roma), Assoc.Prof.Wicharn Lewkeeratiyutkul (Chulalongkorn University, Bangkok), Dr.Rachel Dawe Martins (Istituto Superior Tecnico, Lisboa), Dr.Matti Raasakka (Paris 13 University), Dr.Noppakhun Suthichitranont.
Quantum tomography meets dynamical systems and bifurcations theory
Goyeneche, D., E-mail: dardo.goyeneche@cefop.udec.cl [Departamento de Fisíca, Universidad de Concepción, Casilla 160-C, Concepción, Chile and Center for Optics and Photonics, Universidad de Concepción, Casilla 4012, Concepción (Chile); Torre, A. C. de la [Departamento de Física, Universidad Nacional de Mar del Plata, IFIMAR-CONICET, Dean Funes 3350, 7600 Mar del Plata (Argentina)
2014-06-15T23:59:59.000Z
A powerful tool for studying geometrical problems in Hilbert spaces is developed. We demonstrate the convergence and robustness of our method in every dimension by considering dynamical systems theory. This method provides numerical solutions to hard problems involving many coupled nonlinear equations in low and high dimensions (e.g., quantum tomography problem, existence and classification of Pauli partners, mutually unbiased bases, complex Hadamard matrices, equiangular tight frames, etc.). Additionally, this tool can be used to find analytical solutions and also to implicitly prove the existence of solutions. Here, we develop the theory for the quantum pure state tomography problem in finite dimensions but this approach is straightforwardly extended to the rest of the problems. We prove that solutions are always attractive fixed points of a nonlinear operator explicitly given. As an application, we show that the statistics collected from three random orthonormal bases is enough to reconstruct pure states from experimental (noisy) data in every dimension d ? 32.
Loop Quantum Theory Applied to Biology and Nonlinear Whole Biology
Yi-Fang Chang
2008-01-02T23:59:59.000Z
The loop quantum theory, which constitutes a very small discontinuous space, as new method is applied to biology. The model of protein folding and lungs is proposed. In the model, some known results are used, and four approximate conclusions are obtained: their structures are quantized, their space regions are finite, various singularities correspond to folding and crossed points, and different types of catastrophe exist. Further, based on the inseparability and correlativity of the biological systems, the nonlinear whole biology is proposed, and four basic hypotheses are formed. It may unify reductionism and holism, structuralism and functionalism. Finally, the medical meaning of the theory is discussed briefly.
3D gravity with dust: classical and quantum theory
Viqar Husain; Jonathan Ziprick
2015-06-02T23:59:59.000Z
We study the Einstein gravity and dust system in three spacetime dimensions as an example of a non-perturbative quantum gravity model with local degrees of freedom. We derive the Hamiltonian theory in the dust time gauge and show that it has a rich class of exact solutions. These include the Ba\\~nados-Teitelboim-Zanelli black hole, static solutions with naked singularities and travelling wave solutions with dynamical horizons. We give a complete quantization of the wave sector of the theory, including a definition of a self-adjoint spacetime metric operator. This operator is used to demonstrate the quantization of deficit angle and the fluctuation of dynamical horizons.
Neutron stars in the BPS Skyrme model: mean-field limit vs. full field theory
Adam, C; Sanchez-Guillen, J; Vazquez, R; Wereszczynski, A
2015-01-01T23:59:59.000Z
Using a solitonic model of nuclear matter, the BPS Skyrme model, we compare neutron stars obtained in the full field theory, where gravitational back reaction is completely taken into account, with calculations in a mean-field approximation using the Tolman-Oppenheimer-Volkoff approach. In the latter case, a mean-field-theory equation of state is derived from the original BPS field theory. We show that in the full field theory, where the energy density is non-constant even at equilibrium, there is no universal and coordinate independent equation of state of nuclear matter, in contrast to the mean-field approximation. We also study how neutron star properties are modified by going beyond mean field theory, and find that the differences between mean field theory and exact results can be considerable.
Violation of no signaling in higher order quantum measure theories
Karthik S. Joshi; R. Srikanth; Urbasi Sinha
2013-08-28T23:59:59.000Z
More general probability sum-rules for describing interference than found in quantum mechanics (QM) were formulated by Sorkin in a hierarchy of such rules. The additivity of classical measure theory corresponds to the second sum-rule. QM violates this rule, but satisfies the third and higher sum-rules. This evokes the question of whether there are physical principles that forbid their violation. We show that under certain assumptions, violation of higher sum-rules allows for superluminal signaling.
Towards a double field theory on para-Hermitian manifolds
Vaisman, Izu [Department of Mathematics, University of Haifa, Haifa (Israel)] [Department of Mathematics, University of Haifa, Haifa (Israel)
2013-12-15T23:59:59.000Z
In a previous paper, we have shown that the geometry of double field theory has a natural interpretation on flat para-Kähler manifolds. In this paper, we show that the same geometric constructions can be made on any para-Hermitian manifold. The field is interpreted as a compatible (pseudo-)Riemannian metric. The tangent bundle of the manifold has a natural, metric-compatible bracket that extends the C-bracket of double field theory. In the para-Kähler case, this bracket is equal to the sum of the Courant brackets of the two Lagrangian foliations of the manifold. Then, we define a canonical connection and an action of the field that correspond to similar objects of double field theory. Another section is devoted to the Marsden-Weinstein reduction in double field theory on para-Hermitian manifolds. Finally, we give examples of fields on some well-known para-Hermitian manifolds.
Dynamics of polymers: A mean-field theory
Fredrickson, Glenn H. [Department of Chemical Engineering, University of California, Santa Barbara, California 93106 (United States) [Department of Chemical Engineering, University of California, Santa Barbara, California 93106 (United States); Materials Research Laboratory, University of California, Santa Barbara, California 93106 (United States); Department of Materials, University of California, Santa Barbara, California 93106 (United States); Orland, Henri [Institut de Physique Théorique, CE-Saclay, CEA, F-91191 Gif-sur-Yvette Cedex (France)] [Institut de Physique Théorique, CE-Saclay, CEA, F-91191 Gif-sur-Yvette Cedex (France)
2014-02-28T23:59:59.000Z
We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a Martin-Siggia-Rose (MSR) type description of the exact many-chain dynamics. A saddle point approximation to the generating functional, involving conditions where the MSR action is stationary with respect to a collective density field ? and a conjugate MSR response field ?, produces the desired dynamical mean-field theory. Besides clarifying the proper structure of mean-field theory out of equilibrium, our results have implications for numerical studies of polymer dynamics involving hybrid particle-field simulation techniques such as the single-chain in mean-field method.
On Torsion Fields in Higher Derivative Quantum Gravity
S. I. Kruglov
2008-01-03T23:59:59.000Z
We consider axial torsion fields which appear in higher derivative quantum gravity. It is shown, in general, that the torsion field possesses states with two spins, one and zero, with different masses. The first-order formulation of torsion fields is performed. Projection operators extracting pure spin and mass states are given. We obtain the Lagrangian in the framework of the first order formalism and energy-momentum tensor. The effective interaction of torsion fields with electromagnetic fields is discussed. The Hamiltonian form of the first order torsion field equation is given.
Coherent versus measurement feedback: Linear systems theory for quantum information
Naoki Yamamoto
2014-10-10T23:59:59.000Z
To control a quantum system via feedback, we generally have two options in choosing control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is the measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages/disadvantages, depending on the system and the control goal, hence their comparison in several situation is important. This paper considers a general open linear quantum system with the following specific control goals; back-action evasion (BAE), generation of a quantum non-demolished (QND) variable, and generation of a decoherence-free subsystem (DFS), all of which have important roles in quantum information science. Then some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand it is shown that, for each control goal, there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of BAE, QND, and DFS in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.
A New Look at the Position Operator in Quantum Theory
Felix M. Lev
2015-01-07T23:59:59.000Z
The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory by analogy with classical electrodynamics. As a consequence, an inevitable effect in standard theory is the wave packet spreading (WPS) of the photon coordinate wave function in directions perpendicular to the photon momentum. This leads to the following paradoxes: if the major part of photons emitted by stars are in wave packet states (what is the most probable scenario) then we should see not separate stars but only an almost continuous background from all stars; no anisotropy of the CMB radiation should be observable; data on gamma-ray bursts, signals from directional radio antennas (in particular, in experiments on Shapiro delay) and signals from pulsars show no signs of WPS. In addition, a problem arises why there are no signs of WPS for protons in the LHC ring. We argue that the above postulate is based neither on strong theoretical arguments nor on experimental data and propose a new consistent definition of the position operator. Then WPS in directions perpendicular to the particle momentum is absent and the paradoxes are resolved. Different components of the new position operator do not commute with each other and, as a consequence, there is no wave function in coordinate representation. Implications of the results for entanglement, quantum locality and the problem of time in quantum theory are discussed.
Entanglement entropy in Galilean conformal field theories and flat holography
Arjun Bagchi; Rudranil Basu; Daniel Grumiller; Max Riegler
2014-10-15T23:59:59.000Z
We present the analytical calculation of entanglement entropy for a class of two dimensional field theories governed by the symmetries of the Galilean conformal algebra, thus providing a rare example of such an exact computation. These field theories are the putative holographic duals to theories of gravity in three-dimensional asymptotically flat spacetimes. We provide a check of our field theory answers by an analysis of geodesics. We also exploit the Chern-Simons formulation of three-dimensional gravity and adapt recent proposals of calculating entanglement entropy by Wilson lines in this context to find an independent confirmation of our results from holography.
The hyperbolic field theory on the plane of double variable
Dmitry Pavlov; Sergey Kokarev
2015-01-05T23:59:59.000Z
By analogy to the theory of harmonic fields on the complex plane, we build the theory of wave-like fields on the plane of double variable. We construct the hyperbolic analogues of point vortices, sources, vortice-sources and their higher-order multipole generalizations. We examine the physical aspects and the possibility of extension to the space of polynumbers of higher dimensions.
Geometrical Properties and Propagation for the Proca Field Theory
Luca Fabbri
2009-08-28T23:59:59.000Z
We consider the Proca field with dynamical term given by the exterior derivative with respect to the most general connection; the most general Proca field equations are given, and a discussion about the propagation and the geometrical properties are presented: it is shown that this generalization is inconsistent. So the standard theory is already the most general Proca Theory possible.
Overview of the Theory of Self-Dual Fields
Garfunkel, Eric
and differential K theory · The general self-dual QFT · Open problems. #12;Introduction Chiral fields are very Fermion Indeed, for R2 =2 there are four reps of the chiral algebra: 1, e± i 2 , ei From this viewpoint, the dependence on spin structure is obvious. Free fermion: = ei Self-dual field is equivalent to the theory
Twisted noncommutative field theory with the Wick-Voros and Moyal products
Galluccio, Salvatore; Lizzi, Fedele; Vitale, Patrizia [Dipartimento di Scienze Fisiche, Universita di Napoli Federico II and INFN, Sezione di Napoli Monte S. Angelo, Via Cintia, 80126 Napoli (Italy)
2008-10-15T23:59:59.000Z
We present a comparison of the noncommutative field theories built using two different star products: Moyal and Wick-Voros (or normally ordered). For the latter we discuss both the classical and the quantum field theory in the quartic potential case and calculate the Green's functions up to one loop, for the two- and four-point cases. We compare the two theories in the context of the noncommutative geometry determined by a Drinfeld twist, and the comparison is made at the level of Green's functions and S matrix. We find that while the Green's functions are different for the two theories, the S matrix is the same in both cases and is different from the commutative case.
Quantum Defect Theory for Cold Chemistry with Product Quantum State Resolution
Hazra, Jisha; Bohn, John L; Balakrishnan, N
2014-01-01T23:59:59.000Z
We present a formalism for cold and ultracold atom-diatom chemical reactions that combines a quantum close-coupling method at short-range with quantum defect theory at long-range. The method yields full state-to-state rovibrationally resolved cross sections as in standard close-coupling (CC) calculations but at a considerably less computational expense. This hybrid approach exploits the simplicity of MQDT while treating the short-range interaction explicitly using quantum CC calculations. The method, demonstrated for D+H$_2\\to$ HD+H collisions with rovibrational quantum state resolution of the HD product, is shown to be accurate for a wide range of collision energies and initial conditions. The hybrid CC-MQDT formalism may provide an alternative approach to full CC calculations for cold and ultracold reactions.
Pure Geometric Field Theory: Description of Gravity and Material Distribution
M. I. Wanas; Nabil L. Youssef; W. El Hanafy
2015-03-31T23:59:59.000Z
A field theory is constructed in the context of parameterized absolute parallelism\\linebreak geometry. The theory is shown to be a pure gravity one. It is capable of describing the gravitational field and a material distribution in terms of the geometric structure of the geometry used (the parallelization vector fields). Three tools are used to attribute physical properties to the geometric objects admitted by the theory. Poisson and Laplace equations are obtained in the linearized version of the theory. The spherically symmetric solution of the theory, in free space, is found to coincide with the Schwarzschild exterior solution of the general theory of relativity. The theory respects the weak equivalence principle in free space only. Gravity and material distribution are not minimally coupled.
Effective field theory: A modern approach to anomalous couplings
Degrande, Céline, E-mail: cdegrand@illinois.edu [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States) [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States); Centre for Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium); Greiner, Nicolas [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States) [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States); Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 München (Germany); Kilian, Wolfgang [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States) [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States); University of Siegen, Fachbereich Physik, D-57068 Siegen (Germany); Mattelaer, Olivier [Centre for Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium)] [Centre for Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium); Mebane, Harrison; Stelzer, Tim; Willenbrock, Scott [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States)] [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States); Zhang, Cen [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States) [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, IL 61801 (United States); Centre for Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve (Belgium)
2013-08-15T23:59:59.000Z
We advocate an effective field theory approach to anomalous couplings. The effective field theory approach is the natural way to extend the standard model such that the gauge symmetries are respected. It is general enough to capture any physics beyond the standard model, yet also provides guidance as to the most likely place to see the effects of new physics. The effective field theory approach also clarifies that one need not be concerned with the violation of unitarity in scattering processes at high energy. We apply these ideas to pair production of electroweak vector bosons. -- Highlights: •We discuss the advantages of effective field theories compared to anomalous couplings. •We show that one need not be concerned with unitarity violation at high energy. •We discuss the application of effective field theory to weak boson physics.
GravitoMagnetic Field in Tensor-Vector-Scalar Theory
Exirifard, Qasem, E-mail: exir@theory.ipm.ac.ir [Institute for Research in Fundamental Sciences (IPM), Tehran (Iran, Islamic Republic of)
2013-04-01T23:59:59.000Z
We study the gravitomagnetism in the TeVeS theory. We compute the gravitomagnetic field that a slow moving mass distribution produces in its Newtonian regime. We report that the consistency between the TeVeS gravitomagnetic field and that predicted by the Einstein-Hilbert theory leads to a relation between the vector and scalar coupling constants of the theory. We translate the Lunar Laser Ranging measurement's data into a constraint on the deviation from this relation.
Mehdi Farzanehpour; I. V. Tokatly
2015-06-29T23:59:59.000Z
We use analytic (current) density-potential maps of time-dependent (current) density functional theory (TD(C)DFT) to inverse engineer analytically solvable time-dependent quantum problems. In this approach the driving potential (the control signal) and the corresponding solution of the Schr\\"odinger equation are parametrized analytically in terms of the basic TD(C)DFT observables. We describe the general reconstruction strategy and illustrate it with a number of explicit examples. First we consider the real space one-particle dynamics driven by a time-dependent electromagnetic field and recover, from the general TDDFT reconstruction formulas, the known exact solution for a driven oscillator with a time-dependent frequency. Then we use analytic maps of the lattice TD(C)DFT to control quantum dynamics in a discrete space. As a first example we construct a time-dependent potential which generates prescribed dynamics on a tight-binding chain. Then our method is applied to the dynamics of spin-1/2 driven by a time dependent magnetic field. We design an analytic control pulse that transfers the system from the ground to excited state and vice versa. This pulse generates the spin flip thus operating as a quantum NOT gate.