The Reeh-Schlieder Property for Quantum Fields on Stationary Spacetimes

TL;DR

This paper demonstrates that certain quantum fields on stationary spacetimes possess the Reeh-Schlieder property in ground- and KMS-states, extending to an analog of Borchers' timelike tube theorem for fields like Dirac, Klein-Gordon, and Proca.

Contribution

It establishes the Reeh-Schlieder property for a broad class of quantum fields on stationary spacetimes, including an analog of Borchers' theorem, under hyperbolic equations.

Findings

Reeh-Schlieder property holds for ground- and KMS-states of specified quantum fields

Extension of Borchers' timelike tube theorem to these fields

Applicable to Dirac, Klein-Gordon, and Proca fields

Abstract

We show that as soon as a linear quantum field on a stationary spacetime satisfies a certain type of hyperbolic equation, the (quasifree) ground- and KMS-states with respect to the canonical time flow have the Reeh-Schlieder property. We also obtain an analog of Borchers' timelike tube theorem. The class of fields we consider contains the Dirac field, the Klein-Gordon field and the Proca field.