Continuity of KMS States for Quantum Fields on Manifolds

TL;DR

This paper proves that various important quantum states in curved spacetime are always continuous in the distribution sense, which has implications for the mathematical consistency of quantum field theory in curved backgrounds.

Contribution

It establishes the continuity of pure, quasifree, ground, and KMS states for linear quantum fields on manifolds, a result not previously demonstrated.

Findings

Pure quasifree states are continuous in the distribution sense.

Regular quasifree ground and KMS states are continuous.

Continuity has applications in quantum field theory on curved spacetimes.

Abstract

We show that pure, quasifree states, as well as regular (i.e., those with a unique vacuum) quasifree ground and KMS states, for linear quantum fields in a curved spacetime, are always continuous in the sense of distributions, and provide certain applications of this fact.