Retarded thermal Greens functions and forward scattering amplitudes at two loops

TL;DR

This paper extends the analysis of retarded thermal Green's functions to two loops, providing a diagrammatic approach in terms of forward scattering amplitudes, and demonstrates infrared singularity cancellation in QED_2.

Contribution

It introduces a simple diagrammatic description for two-loop retarded Green's functions at finite temperature applicable to various field theories.

Findings

Infrared singularities cancel in QED_2 at two loops with vanishing electron mass.

The approach generalizes to scalar field theory and QED.

Provides a method to analyze temperature-dependent parts of Green's functions.

Abstract

In this paper, we extend our earlier one loop analysis to two loops and give a simple diagrammatic description for the retarded Greens functions at finite temperature, in terms of forward scattering amplitudes of on-shell thermal particles. We present a simple discussion, which can be easily generalized to any field theory, of the temperature dependent parts of the retarded two and three point functions in scalar field theory and QED. As an application of our result at two loops, we show how the infrared singularities in the thermal part of the retarded photon self-energy, cancel in QED_2 in the limit of vanishing electron mass.