Microlocal analysis of quantum fields on curved spacetimes: Analytic wavefront sets and Reeh-Schlieder theorems

TL;DR

This paper demonstrates that the Reeh-Schlieder property applies to quantum field states on real analytic spacetimes under an analytic microlocal spectrum condition, extending the understanding of quantum fields in curved spacetime.

Contribution

It establishes the Reeh-Schlieder property under a new analytic microlocal spectrum condition without specific equations of motion, and simplifies conditions for quasifree Klein-Gordon states.

Findings

Reeh-Schlieder property holds for states satisfying the analytic microlocal spectrum condition.

Equivalence of the microlocal spectrum condition to simpler conditions for quasifree states.

Ground- or KMS-states of Klein-Gordon field satisfy the microlocal spectrum condition.

Abstract

We show in this article that the Reeh-Schlieder property holds for states of quantum fields on real analytic spacetimes if they satisfy an analytic microlocal spectrum condition. This result holds in the setting of general quantum field theory, i.e. without assuming the quantum field to obey a specific equation of motion. Moreover, quasifree states of the Klein-Gordon field are further investigated in this work and the (analytic) microlocal spectrum condition is shown to be equivalent to simpler conditions. We also prove that any quasifree ground- or KMS-state of the Klein-Gordon field on a stationary real analytic spacetime fulfills the analytic microlocal spectrum condition.