Localization Regions of Local Observables

TL;DR

This paper demonstrates that in quantum field theories with local observables, each observable can be associated with a minimal localization region, using the Jost-Lehmann-Dyson representation, and explores conditions for their commutativity.

Contribution

It establishes the existence of smallest localization regions for local observables in higher-dimensional quantum field theories and provides criteria for their spacelike commutativity.

Findings

Existence of minimal localization regions for observables.

Conditions for spacelike commutativity of observables.

Extension of localization concepts in algebraic quantum field theory.

Abstract

Exploiting the properties of the Jost-Lehmann-Dyson representation, it is shown that in 1+2 or more spacetime dimensions, a nonempty smallest localization region can be associated with each local observable (except for the c-numbers) in a theory of local observables in the sense of Araki, Haag, and Kastler. Necessary and sufficient conditions are given that observables with spacelike separated localization regions commute (locality of the net alone does not yet imply this).