Microlocal analysis of quantum fields on curved space–times: Analytic wave front sets and Reeh–Schlieder theorems

We show in this article that the Reeh–Schlieder property holds for states of quantum fields on real analytic curved space–times 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 the present 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 space–time fulfills the analytic microlocal spectrum condition.