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Gauge Theories at finite temperature

Abstract

Gauge theories, like Quantum Electrodynamics (QED), Quantum Chromodynamics (QCD) and Gravity, are the theoretical basis for the study of the fudamental interactions of elementary particles. When the effects of the temperature are considered, the basic structure of matter reveals itself as a plasma of leptons and quarks interacting with quanta of photons and gluons. The dynamics of these particles is described by field theories whose common characteristic is the symmetry under gauge transformations. Gauge theories are also relevant in 2 + 1 dimensions, where they describe properties of the condensed matter, such as the quantum Hall efrfect and supercondutivity. An important property of these theories is the possibility to consider in the effective action the presence of the topological Chern-Simons (CS) terms. At zero temperature, such terms imply a quantization law, which preserves the invariance under large gauge transformations, associated with nontrivial topological numbers. On the other hand, at nonzero temperatures T, each term of the perturbative series is a continuous function of T, which, consequently, cannot be quantized. Nevertheless, as we have shown in previous works, in certain cases the complete action can be rendered invariant under large gauge transformations. This happens because the CS coefficient represents only the first term in the expansion of the effective action at finite temprature. This project, which represents a development of our work, has the objective of studying the mechanism that ensure the large gauge invariance of QED and QCD in the presence of topological terms at finite temperature. We would like to investigate these processes in physical gauges, like the axial and Coulomb gauges, where the vector bosons have only physical degrees of fredom. We expect that the use of such gauges at finite temperature, may reveal more clearly the mechanism that ensures the large gauge invariance of these theories. (AU)

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