On the Reeh-Schlieder Property in Curved Spacetime

TL;DR

This paper investigates the existence of Reeh-Schlieder states in curved spacetimes within locally covariant quantum field theory, showing that physically relevant states with a weak Reeh-Schlieder property always exist.

Contribution

It introduces a spacetime deformation approach to establish the existence of Reeh-Schlieder states in curved spacetimes, extending prior results.

Findings

Physically interesting states with a weak Reeh-Schlieder property always exist.

Algebraic states with full Reeh-Schlieder property also exist but may lack physical relevance.

Abstract

We attempt to prove the existence of Reeh-Schlieder states on curved spacetimes in the framework of locally covariant quantum field theory using the idea of spacetime deformation and assuming the existence of a Reeh-Schlieder state on a diffeomorphic (but not isometric) spacetime. We find that physically interesting states with a weak form of the Reeh-Schlieder property always exist and indicate their usefulness. Algebraic states satisfying the full Reeh-Schlieder property also exist, but are not guaranteed to be of physical interest.