Local incompatibility of the microlocal spectrum condition with the KMS property along spacelike directions in quantum field theory on curved spacetime

TL;DR

This paper demonstrates that in curved spacetime quantum field theory, states satisfying the KMS condition cannot meet a specific microlocal condition at points where the Killing vector field is spacelike, highlighting a local incompatibility.

Contribution

It reveals a local incompatibility between the KMS condition and a microlocal spectrum condition in curved spacetime quantum fields.

Findings

KMS states cannot satisfy the microlocal condition at spacelike points.

The incompatibility is localized to points with spacelike Killing vectors.

The result applies to states weaker than the usual microlocal spectrum condition.

Abstract

States of a generic quantum field theory on a curved spacetime are considered which satisfy the KMS condition with respect to an evolution associated with a complete (Killing) vector field. It is shown that at any point where the vector field is spacelike, such states cannot satisfy a certain microlocal condition which is weaker than the microlocal spectrum condition in the case of asymptotically free fields.