Relativistic KMS-condition and Kaellen-Lehmann type representatios of thermal propagators

TL;DR

This paper introduces a relativistic KMS condition that characterizes thermal equilibrium states in quantum field theory, leading to a Kaellen-Lehmann type representation of thermal propagators with specific regularity properties.

Contribution

It generalizes the KMS condition to a relativistic setting and derives a new representation for thermal propagators, connecting thermal and vacuum spectral conditions.

Findings

Established a relativistic KMS condition for thermal states

Derived a Kaellen-Lehmann type representation for thermal propagators

Outlined potential applications and open problems in the field

Abstract

A relativistic version of the Kubo--Martin--Schwinger boundary condition is presented which fixes the properties of thermal equilibrium states with respect to arbitrary space--time translations. This novel condition is a natural generalization of the relativistic spectrum condition in the vacuum theory and has similar consequences. In combination with the condition of locality it gives rise to a Kaellen--Lehmann type representation of thermal propagators with specific regularity properties. Possible applications of the results and some open problems are outlined.