The split property for locally covariant quantum field theories in curved spacetime

TL;DR

This paper extends the split property of quantum field theories from flat to curved spacetimes, using deformation techniques, and explores its implications for local algebras and gauge symmetries.

Contribution

It introduces a method to transfer the split property to curved spacetimes and constructs states satisfying key properties, advancing the understanding of local quantum field theory structures.

Findings

Split property holds in curved spacetimes via deformation arguments.

States with split and Reeh-Schlieder properties can be constructed.

Conditions for local gauge generators and algebra classification are established.

Abstract

The split property expresses the way in which local regions of spacetime define subsystems of a quantum field theory. It is known to hold for general theories in Minkowski space under the hypothesis of nuclearity. Here, the split property is discussed for general locally covariant quantum field theories in arbitrary globally hyperbolic curved spacetimes, using a spacetime deformation argument to transport the split property from one spacetime to another. It is also shown how states obeying both the split and (partial) Reeh-Schlieder properties can be constructed, providing standard split inclusions of certain local von Neumann algebras. Sufficient conditions are given for the theory to admit such states in ultrastatic spacetimes, from which the general case follows. A number of consequences are described, including the existence of local generators for global gauge transformations, and the classification of certain local von Neumann algebras. Similar arguments are applied to the distal split property and circumstances are exhibited under which distal splitting implies the full split property.