Retarded Greens Functions and Forward Scattering Amplitudes in Thermal Field Theory

TL;DR

This paper introduces a diagrammatic method to relate retarded vertex functions in real-time thermal field theory to forward scattering amplitudes, simplifying calculations and revealing that temperature-dependent parts vanish in certain models.

Contribution

It provides a simple diagrammatic identification and calculational method for retarded vertex functions in thermal field theory, linking them to forward scattering amplitudes and showing their vanishing in specific cases.

Findings

Temperature dependent parts of retarded functions vanish at one loop in 1+1 dimensional massless QED.

The method simplifies evaluating temperature effects in thermal field theory.

In massless QED, these parts vanish to all orders in perturbation theory.

Abstract

In this paper, we give a simple diagrammatic identification of the unique combination of the causal n-point vertex functions in the real time formalism that would coincide with the corresponding functions obtained in the imaginary time formalism. Furthermore, we give a simple calculational method for evaluating the temperature dependent parts of the retarded vertex functions, to one loop, by identifying them with the forward scattering amplitudes of on-shell thermal particles. As an application of the method, we calculate and show that the temperature dependent parts of all the retarded functions vanish at one loop order for 1+1 dimensional massless QED. We further point out that, in this model, in fact, the temperature dependent parts of all the retarded vertex functions vanish to all orders in perturbation theory.