Three-Point Functions at Finite Temperature

TL;DR

This paper develops a framework for analyzing three-point correlation functions at finite temperature using the closed time path formalism, providing spectral representations and simplified computational methods.

Contribution

It introduces a decomposition of the tensor components into seven vertex functions and derives spectral representations, simplifying real-time calculations at finite temperature.

Findings

Decomposition of eight tensor components into seven vertex functions

Spectral representation in terms of two real spectral functions

Simplified vertex tensor for real-time calculations

Abstract

We study 3-point functions at finite temperature in the closed time path formalism. We give a general decomposition of the eight component tensor in terms of seven vertex functions. We derive a spectral representation for these seven functions in terms of two independent real spectral functions. We derive relationships between the seven functions and obtain a representation of the vertex tensor that greatly simplifies calculations in real time.