Thermal Operator Representation of Finite Temperature Graphs

TL;DR

This paper demonstrates a simple method to relate finite temperature Feynman graphs to zero temperature diagrams using a thermal operator, applicable in both imaginary and real time formalisms, and extends it to include chemical potential effects.

Contribution

It introduces a straightforward thermal operator approach that connects finite temperature graphs to zero temperature diagrams, including cases with nontrivial chemical potential.

Findings

Finite temperature graphs are related to zero temperature diagrams via a thermal operator.

The method applies to both imaginary time and real time formalisms.

The approach is generalized to include nontrivial chemical potentials.

Abstract

Using the mixed space representation (t,p) in the context of scalar field theories, we prove in a simple manner that the Feynman graphs at finite temperature are related to the corresponding zero temperature diagrams through a simple thermal operator, both in the imaginary time as well as in the real time formalisms. This result is generalized to the case when there is a nontrivial chemical potential present. Several interesting properties of the thermal operator are also discussed.