Perturbative Quantum Field Theory at Positive Temperatures: An Axiomatic Approach

TL;DR

This paper demonstrates that perturbative correlation functions in relativistic quantum field theory at finite temperature are uniquely defined by axioms and equations of motion, deriving explicit expressions without using canonical formalism or field doubling.

Contribution

It provides an axiomatic derivation of perturbative expansions at finite temperature, avoiding canonical formalism and field doubling, and highlights an open problem on their existence.

Findings

Explicit sum over generalized Feynman graphs derived

Perturbative expansions uniquely determined by axioms and equations of motion

No canonical formalism or field doubling used

Abstract

It is shown that the perturbative expansions of the correlation functions of a relativistic quantum field theory at finite temperature are uniquely determined by the equations of motion and standard axiomatic requirements, including the KMS condition. An explicit expression as a sum over generalized Feynman graphs is derived. The canonical formalism is not used, and the derivation proceeds from the beginning in the thermodynamic limit. No doubling of fields is invoked. An unsolved problem concerning existence of these perturbative expressions is pointed out.