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Title: Confinement criterion for gauge theories with matter fields

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 96; Journal Issue: 9; Related Information: CHORUS Timestamp: 2017-11-27 10:29:15; Journal ID: ISSN 2470-0010
American Physical Society
Country of Publication:
United States

Citation Formats

Greensite, Jeff, and Matsuyama, Kazue. Confinement criterion for gauge theories with matter fields. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.96.094510.
Greensite, Jeff, & Matsuyama, Kazue. Confinement criterion for gauge theories with matter fields. United States. doi:10.1103/PhysRevD.96.094510.
Greensite, Jeff, and Matsuyama, Kazue. Mon . "Confinement criterion for gauge theories with matter fields". United States. doi:10.1103/PhysRevD.96.094510.
title = {Confinement criterion for gauge theories with matter fields},
author = {Greensite, Jeff and Matsuyama, Kazue},
abstractNote = {},
doi = {10.1103/PhysRevD.96.094510},
journal = {Physical Review D},
number = 9,
volume = 96,
place = {United States},
year = {Mon Nov 27 00:00:00 EST 2017},
month = {Mon Nov 27 00:00:00 EST 2017}

Journal Article:
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This content will become publicly available on November 27, 2018
Publisher's Accepted Manuscript

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  • In a solvable model of two-dimensional SU(N) (N{r_arrow}{infinity}) gauge fields interacting with matter in both adjoint and fundamental representations we investigate the nature of the phase transition separating the strong and weak coupling regions of the phase diagram. By interpreting the large N solution of the model in terms of SU(N) representations it is shown that the strong coupling phase corresponds to a region where a gap occurs in the spectrum of irreducible representations. We identify a gauge-invariant order parameter for the generalized confinement-deconfinement transition and give a physical meaning to each phase in terms of the interaction of amore » pair of test charges. {copyright} {ital 1997} {ital The American Physical Society}« less
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  • Ising lattice gauge theory with matter fields is generalized to a family of gauge-invariant N-state models. These models are soluble in the N ..-->.. infinity limit. In both two and three spatial dimensions the N ..-->.. infinity limits of these models possess three phases separated by lines of first-order transitions. One phase admits free charge, the second confines, and the third experiences the Higgs phenomenon. 1/N corrections are calculable and terminate the boundary between the confining and Higgs phases. A closed region of free charge persists for all N > or = 1.
  • We consider the SL(2,C)-covariant Lagrangian formulation of gravitational theories with the presence of spinor matter fields. The invariance properties of such theories give rise to the conservation laws (the contracted Bianchi identities) having in the presence of matter fields a more complicated form than those known in the literature previously. A general SL(2,C) gauge theory of gravity is cast into an SL(2,C)-covariant Hamiltonian formulation. Breaking the SL(2,C) symmetry of the system to the SU(2) symmetry, by introducing a spacelike slicing of spacetime, we get an SU(2)-covariant Hamiltonian picture. The qualitative analysis of SL(2,C) gauge theories of gravity in the SU(2)-covariantmore » formulation enables us to define the dynamical symplectic variables and the gauge variables of the theory under consideration as well as to divide the set of field equations into the dynamical equations and the constraints. In the SU(2)-covariant Hamiltonian formulation the primary constraints, which are generic for first-order matter Lagrangians (Dirac, Weyl, Fierz-Pauli), can be reduced. The effective matter symplectic variables are given by SU(2)-spinor-valued half-forms on three-dimensional slices of spacetime. The coupled Einstein-Cartan-Dirac (Weyl, Fierz-Pauli) system is analyzed from the (3+1) point of view. This analysis is complete; the field equations of the Einstein-Cartan-Dirac theory split into 18 gravitational dynamical equations, 8 dynamical Dirac equations, and 7 first-class constraints. The system has 4+8 = 12 independent degrees of freedom in the phase space.« less
  • The A/sub 0/ = 0 canonical formalism is shown to be completely consistent even though Gauss's law is not verified as a field equation. This is so because the Hilbert space of states must also involve states coupled with external static charge distributions. Indeed these cannot be handled by adding the standard A/sub ext//sub term because it vanishes identically in the A/sub 0/ = 0 gauge for static charges. The corresponding charge densities are instead the eigenvalues of the operator of infinitesimal time-independent gauge transformations which commute with the Hamiltonian. The implications of this viewpoint are discussed inmore » connection with Gribov's phenomenon, the theta vacuum, perturbation theory, and quark confinement. The constant of motion due to gauge invariance in gauge theories plays the same role as the constant of motion due to translational invariance in soliton quantization.« less