Axiomatic Analyticity Properties and Representations of Particles in Thermal Quantum Field Theory

TL;DR

This paper develops an axiomatic framework for thermal quantum field theory, establishing analyticity properties of n-point functions and generalizing the Källén-Lehmann representation to finite temperature scenarios.

Contribution

It introduces a new axiomatic approach to thermal QFT, extending fundamental properties known from vacuum QFT to finite temperature cases.

Findings

Analyticity properties of n-point functions at finite temperature

Generalized Källén-Lehmann representation for propagators

Discussion of thermal quasiparticles and hard-thermal-loop calculations

Abstract

We provide an axiomatic framework for Quantum Field Theory at finite temperature which implies the existence of general analyticity properties of the $ n $-point functions; the latter parallel the properties derived from the usual Wightman axioms in the vacuum representation of Quantum Field Theory. Complete results are given for the propagators, including a generalization of the K\"all\'en-Lehmann representation. Some known examples of ``hard-thermal-loop calculations'' and the representation of ``quasiparticles'' are discussed in this general framework.