Punctured Haag duality in locally covariant quantum field theories

TL;DR

This paper introduces and analyzes punctured Haag duality, a property of local algebra nets in quantum field theories on curved spacetimes, showing its equivalence to Haag duality under local covariance, with the free Klein-Gordon field as an example.

Contribution

It defines punctured Haag duality and proves its equivalence to Haag duality in locally covariant quantum field theories, with explicit example verification.

Findings

Punctured Haag duality implies Haag duality and local definiteness.

In locally covariant theories, the converse also holds, establishing equivalence.

The free Klein-Gordon field satisfies punctured Haag duality.

Abstract

We investigate a new property of nets of local algebras over 4-dimensional globally hyperbolic spacetimes, called punctured Haag duality. This property consists in the usual Haag duality for the restriction of the net to the causal complement of a point $p$ of the spacetime. Punctured Haag duality implies Haag duality and local definiteness. Our main result is that, if the theory is locally covariant in the sense of Brunetti, Fredenhagen and Verch, then also the converse holds. The free Klein-Gordon field provides an example in which this property is verified.