Local Thermal Equilibrium and KMS states in Curved Spacetime

TL;DR

This paper investigates the properties of KMS states in curved spacetime, showing they may not always have a well-defined local temperature, and proposes criteria and definitions for local thermal equilibrium in quantum field theory.

Contribution

It introduces a criterion for local thermal equilibrium with sharp temperature and a new way to define thermal energy in KMS states in curved spacetime.

Findings

KMS states can lack a definite local temperature in curved spacetime.

A criterion for identifying LTE states with sharp local temperature is proposed.

A relation between local temperature and the KMS parameter  is established in (Anti) de Sitter spacetime.

Abstract

On the example of a free massless and conformally coupled scalar field, it is argued that in quantum field theory in curved spacetimes with time-like Killing field, the corresponding KMS states (generalized Gibbs ensembles) at parameter \beta>0 need not possess a definite temperature in the sense of the zeroth law. In fact, these states, although passive in the sense of the second law, are not always in local thermal equilibrium (LTE). A criterion characterizing LTE states with sharp local temperature is discussed. Moreover, a proposal is made for fixing the renormalization freedom of composite fields which serve as "thermal observables" and a new definition of the thermal energy of LTE states is introduced. Based on these results a general relation between the local temperature and the parameter \beta\ is established for KMS states in (Anti) de Sitter spacetime.