Analytic states in quantum field theory on curved spacetimes

TL;DR

This paper explores the properties of quantum field states in curved spacetimes, demonstrating that certain analyticity conditions lead to important algebraic and structural results similar to those in flat spacetime quantum field theory.

Contribution

It extends the timelike tube theorem and Reeh-Schlieder property to curved spacetimes under analyticity assumptions, generalizing previous flat spacetime results.

Findings

Timelike tube theorem holds in real analytic curved spacetimes.

Reeh-Schlieder property is valid for states with microlocal analyticity.

Algebraic structures of quantum fields are preserved under deformation in curved backgrounds.

Abstract

We discuss high energy properties of states for (possibly interacting) quantum fields in curved spacetimes. In particular, if the spacetime is real analytic, we show that an analogue of the timelike tube theorem and the Reeh-Schlieder property hold with respect to states satisfying a weak form of microlocal analyticity condition. The former means the von Neumann algebra of observables of a spacelike tube equals the von Neumann algebra of observables of a significantly bigger region, that is obtained by deforming the boundary of the tube in a timelike manner. This generalizes theorems by Borchers and Araki to curved spacetimes.