Thermal Green's functions from quantum-mechanical path integrals. II. Inclusion of fermions

doi:https://doi.org/10.1103/PhysRevD.49.1047

Title: Thermal Green's functions from quantum-mechanical path integrals. II. Inclusion of fermions

Full Record
Other Related Research

Abstract

In a previous paper we have shown how, for bosonic fields, the generating functional in both relativistic quantum field theory and thermal field theory can be evaluated by use of a standard quantum-mechanical path integral. In this paper we extend this method to include fermionic fields. A particular problem is posed by Green's functions with external fermionic lines, where the different boundary conditions of bosons and fermions in imaginary time have to be accommodated within one path integral expression. The general procedure is worked out in the example of scalar and spinor self-energies in a simple model with a Yukawa coupling of a scalar to a Majorana spinor.

Authors:

McKeon, D G.C. ^[1]; Rebhan, A K ^[2]

Department of Applied Mathematics, University of Western Ontario, London, Ontario, N6A5B7 (Canada)
Fakultaet fuer Physik, Universitaet Bielefeld, D-33501 Bielefeld (Germany)

Publication Date:: 1994-01-15

OSTI Identifier:: 5410410

Resource Type:: Journal Article

Journal Name:: Physical Review, D (Particles Fields); (United States)

Additional Journal Information:: Journal Volume: 49:2; Journal ID: ISSN 0556-2821

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; GREEN FUNCTION; QUANTUM MECHANICS; FERMIONS; FEYNMAN PATH INTEGRAL; BOSONS; BOUNDARY CONDITIONS; QUANTUM FIELD THEORY; SELF-ENERGY; YUKAWA POTENTIAL; ENERGY; FIELD THEORIES; FUNCTIONS; INTEGRALS; MECHANICS; NUCLEAR POTENTIAL; POTENTIALS; 662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)

Citation Formats


                    McKeon, D G.C., and Rebhan, A K. Thermal Green's functions from quantum-mechanical path integrals. II. Inclusion of fermions.  United States: N. p., 1994. 
        Web.  doi:10.1103/PhysRevD.49.1047.

Copy to clipboard


                    McKeon, D G.C., & Rebhan, A K. Thermal Green's functions from quantum-mechanical path integrals. II. Inclusion of fermions.  United States.  https://doi.org/10.1103/PhysRevD.49.1047

Copy to clipboard


                    McKeon, D G.C., and Rebhan, A K. Sat .  
        "Thermal Green's functions from quantum-mechanical path integrals. II. Inclusion of fermions".  United States.  https://doi.org/10.1103/PhysRevD.49.1047.

Copy to clipboard


                    
@article{osti_5410410,

  title        = {Thermal Green's functions from quantum-mechanical path integrals. II. Inclusion of fermions},

  author       = {McKeon, D G.C. and Rebhan, A K},

  abstractNote = {In a previous paper we have shown how, for bosonic fields, the generating functional in both relativistic quantum field theory and thermal field theory can be evaluated by use of a standard quantum-mechanical path integral. In this paper we extend this method to include fermionic fields. A particular problem is posed by Green's functions with external fermionic lines, where the different boundary conditions of bosons and fermions in imaginary time have to be accommodated within one path integral expression. The general procedure is worked out in the example of scalar and spinor self-energies in a simple model with a Yukawa coupling of a scalar to a Majorana spinor.},

  doi          = {10.1103/PhysRevD.49.1047},

  url          = {https://www.osti.gov/biblio/5410410},
  journal      = {Physical Review, D (Particles Fields); (United States)},

  issn         = {0556-2821},

  number       = ,

  volume       = 49:2,

  place        = {United States},

  year         = {1994},

  month        = {1}

}

Copy to clipboard

Journal Article:

https://doi.org/10.1103/PhysRevD.49.1047

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

Thermal Green's functions from quantum-mechanical path integrals

Journal Article McKeon, D G.C. ; Rebhan, A - Physical Review, D (Particles Fields); (United States)

In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum-mechanical path integral. With this calculational approach one avoids the loop-momentum integrals usually encountered in Feynman perturbation theory, although with thermal Green's functions, a discrete sum (over the winding numbers of paths with respect to the circular imaginary time) must be computed. The high-temperature expansion of this sum can be performed for all Green's functions at the same time, and is particularly simple for the static case. The proceduremore »« less
https://doi.org/10.1103/PhysRevD.47.5487
On using the quantum mechanical path integral in quantum field theory

Journal Article McKeon, D G.C. - Annals of Physics (New York); (United States)

It is shown how matrix elements of the form [l angle]x[vert bar]e[sup [minus]iHt][vert bar]y[r angle], which arise in closed-form expressions for the generating functional, can be evaluated perturbatively using a path integral encountered in the quantum mechanics of a single particle. This allows one to compute Green's functions without ever having to evaluate loop-momentum integrals. This technique is illustrated by considering, in the context of operator regulatization, the vacuum polarization in scalar and spinor electrodynamics to one-loop order, the two-point function in [phi][sup 3][sub 6] theory to two-loop order, the spinor self-energy in massless electrodynamics to one-loop order, the two-pointmore »« less
https://doi.org/10.1006/aphy.1993.1042
Excited states of bosons and fermions in a four-fermi quantum field theory

Journal Article Furlan, P ; Raczka, R - Ann. Phys. (N.Y.); (United States)

A scalar-pseudoscalar four-Fermi quantum field model in four dimensional space-time is considered. Introducing the scalar and pseudoscalar collective bosons, the path-integral representation for the generating functional for Green's functions in terms of the effective total action integral containing only collective bosons is expressed. Using a classical ground-state solution for collective bosons, a new formula for the generating functional for collective boson and fermion Green functions in terms of the effective propagators is derived. It is shown by a partly nonperturbative analysis that the excited states of collective bosons do exist and form finite trajectories in the plane mass-square-spin. These trajectoriesmore »« less
https://doi.org/10.1016/0003-4916(83)90200-2
Nonequilibrium quantum fields: Closed-time-path effective action, Wigner function, and Boltzmann equation

Journal Article Calzetta, E ; Hu, B L - Phys. Rev. D; (United States)

This is the first of a series of papers which describe the functional-integral approach to the study of the statistical and kinetic properties of nonequilibrium quantum fields in flat and curved spacetimes. In this paper we treat a system of self-interacting bosons described by lambdaphi/sup 4/ scalar fields in flat space. We adopt the closed-time-path (CTP or ''in-in'') functional formalism and use a two-particle irreducible (2PI) representation for the effective action. These formalisms allow for a full account of the dynamics of quantum fields, and put the correlation functions on an equal footing with the mean fields. By assuming amore »« less
https://doi.org/10.1103/PhysRevD.37.2878
Braiding statistics and link invariants of bosonic/fermionic topological quantum matter in 2+1 and 3+1 dimensions

Journal Article Putrov, Pavel ; Wang, Juven ; Yau, Shing-Tung - Annals of Physics

Topological Quantum Field Theories (TQFTs) pertinent to some emergent low energy phenomena of condensed matter lattice models in 2+1 and 3+1 dimensions are explored. Many of our TQFTs are highly-interacting without free quadratic analogs. Some of our bosonic TQFTs can be regarded as the continuum field theory formulation of Dijkgraaf–Witten twisted discrete gauge theories. Other bosonic TQFTs beyond the Dijkgraaf–Witten description and all fermionic TQFTs (namely the spin TQFTs) are either higher-form gauge theories where particles must have strings attached, or fermionic discrete gauge theories obtained by gauging the fermionic Symmetry-Protected Topological states (SPTs). We analytically calculate both the Abelianmore »« less
Cited by 38
https://doi.org/10.1016/j.aop.2017.06.019

Full Text Available

Similar Records