Nonperturbative Aspects of Gauge Theories in Thermodynamic Equilibrium in the Matsubara-Fradkin Formalism

Abstract

In this project we study nonperturbative aspects of gauge theories in thermodynamic equilibrium in the Matsubara-Fradkin formalism. We will study generalized quantum electrodynamics (GQED), the gauged Thirring model (GTM) and non-Abelian gauge theories, such as quantum chromodynamics (QCD). Our nonperturbative approaches are both the development and application of Fradkin's modified perturbation theory for the thermodynamic equilibrium problems and the search for nonperturbative approximations for solutions of the Dyson-Schwinger-Fradkin equations with thermal effects. GQED is an extension of Maxwell theory which preserves its two main symmetries and exhibits measurable, distinctive phenomenological implications. For this theory we will also study some questions related with its classical version which were not so far properly addressed in the literature. GTM is a solvable field theory in (1+1)-dimensions which shows two other solvable models as its limits: the Thirring and the Schwinger models. The later exhibits fermion confinement and dynamical mass generation. Moreover, these models also show the bosonization phenomenon. Since the exact solution for these models are known, they are, for our purposes, perfect test models for the efficiency of the nonperturbative techniques we plan to study. Besides describing quark-gluon plasma, QCD also presents one of the major theoretical challenges of the contemporary physics: the description of quark and gluon confinement. Such low-energy regime cannot be studied with perturbation theory. Nonperturbative approaches must be developed.