Finite Temperature Effective Actions

TL;DR

This paper introduces a direct method to compute the exact fermion propagator at finite temperature, enabling the derivation of effective actions in quantum field theories, with applications to 0+1 dimensional QED and the Schwinger model.

Contribution

It provides a novel first-principles approach for evaluating finite temperature effective actions, including explicit calculations for specific models.

Findings

Complete one-loop finite temperature effective actions derived for 0+1 dimensional QED and the Schwinger model.

Retarded and advanced amplitudes vanish in these theories at finite temperature.

The method systematically reproduces all thermal perturbation theory amplitudes.

Abstract

We present, from first principles, a direct method for evaluating the exact fermion propagator in the presence of a general background field at finite temperature, which can be used to determine the finite temperature effective action for the system. As applications, we determine the complete one loop finite temperature effective actions for 0+1 dimensional QED as well as the Schwinger model. These effective actions, which are derived in the real time (closed time path) formalism, generate systematically all the Feynman amplitudes calculated in thermal perturbation theory and also show that the retarded (advanced) amplitudes vanish in these theories.