Adiabatic vacuum states on general spacetime manifolds: Definition, construction, and physical properties

TL;DR

This paper generalizes the concept of adiabatic vacuum states from Robertson-Walker spacetimes to arbitrary globally hyperbolic manifolds using Sobolev wavefront sets, and explores their physical properties and explicit constructions.

Contribution

It extends the definition of adiabatic vacua to general spacetimes and includes applicability to interacting fields, also analyzing their physical properties and providing explicit constructions.

Findings

Adiabatic vacua are defined on general spacetimes using Sobolev wavefront sets.

Hadamard states are a special subclass of adiabatic vacua.

Explicit constructions are provided for manifolds with compact Cauchy surfaces.

Abstract

Adiabatic vacuum states are a well-known class of physical states for linear quantum fields on Robertson-Walker spacetimes. We extend the definition of adiabatic vacua to general spacetime manifolds by using the notion of the Sobolev wavefront set. This definition is also applicable to interacting field theories. Hadamard states form a special subclass of the adiabatic vacua. We analyze physical properties of adiabatic vacuum representations of the Klein-Gordon field on globally hyperbolic spacetime manifolds (factoriality, quasiequivalence, local definiteness, Haag duality) and construct them explicitly, if the manifold has a compact Cauchy surface.