Local Thermal Equilibrium in Quantum Field Theory on Flat and Curved Spacetimes

TL;DR

This paper investigates the existence and properties of local thermal equilibrium states in quantum field theory on both flat and curved spacetimes, highlighting necessary modifications for curved backgrounds and establishing conditions for LTE states.

Contribution

It demonstrates the existence of LTE states in Minkowski spacetime for finite thermal observables and proposes a modified definition of LTE in curved spacetime with existence results under certain assumptions.

Findings

LTE states exist in Minkowski spacetime for finite thermal observables

Modified LTE definition is needed for curved spacetime

Existence of LTE states in curved spacetime is established under specific assumptions

Abstract

The existence of local thermal equilibrium (LTE) states for quantum field theory in the sense of Buchholz, Ojima and Roos is discussed in a model-independent setting. It is shown that for spaces of finitely many independent thermal observables there always exist states which are in LTE in any compact region of Minkowski spacetime. Furthermore, LTE states in curved spacetime are discussed and it is observed that the original definition of LTE on curved backgrounds given by Buchholz and Schlemmer needs to be modified. Under an assumption related to certain unboundedness properties of the pointlike thermal observables, existence of states which are in LTE at a given point in curved spacetime is established. The assumption is discussed for the sets of thermal observables for the free scalar field considered by Schlemmer and Verch.