Haag Duality in the Thermal Sector

TL;DR

This paper proves a generalized Haag duality property for the algebraic structure of a real scalar quantum field in thermal equilibrium on Minkowski spacetime, extending previous ground-state results using purification methods.

Contribution

It introduces a generalized Haag duality result for thermal states of quantum fields, combining ground-state techniques with purification methods.

Findings

Established generalized Haag duality in the KMS representation

Extended duality results from ground states to thermal states

Used purification techniques to prove the duality property

Abstract

We prove that the net of localised von Neumann algebras associated with a real scalar field propagating on Minkowski spacetime, in the KMS representation, satisfies a generalised version of Haag duality. Our proof combines ideas from existing arguments for the ground-state representation with purification techniques.