Effective actions at finite temperature

TL;DR

This paper introduces a direct method to evaluate the exact fermion propagator at finite temperature, enabling the derivation of effective actions for specific models and clarifying amplitude behaviors in thermal field theory.

Contribution

It presents a first-principles approach for calculating finite temperature effective actions and applies it to 0+1 dimensional QED and the Schwinger model, revealing systematic amplitude generation.

Findings

Derived complete one-loop finite temperature effective actions.

Showed retarded and advanced amplitudes vanish in these models.

Demonstrated the method's consistency with thermal perturbation theory.

Abstract

This is a more detailed version of our recent paper where we proposed, from first principles, a direct method for evaluating the exact fermion propagator in the presence of a general background field at finite temperature. This can, in turn, be used to determine the finite temperature effective action for the system. As applications, we discuss the complete one loop finite temperature effective actions for 0+1 dimensional QED as well as for the Schwinger model in detail. 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. Various other aspects of the problem are also discussed in detail.