Wedge-Local Quantum Fields and Noncommutative Minkowski Space

TL;DR

This paper explores a noncommutative quantum field model on Minkowski space, demonstrating wedge-shaped localization, covariance, and non-trivial scattering, while also addressing limitations in sharper localization observables.

Contribution

It introduces a wedge-local quantum field framework on noncommutative Minkowski space with consistent symmetry and localization properties, and analyzes its scattering behavior.

Findings

Fields labeled by noncommutativity parameters related by Lorentz transformations

Fields localized in spacelike separated wedges commute

Two-particle S-matrix elements are non-trivial

Abstract

Within the setting of a recently proposed model of quantum fields on noncommutative Minkowski spacetime, the consequences of the consistent application of the proper, untwisted Poincare group as the symmetry group are investigated. The emergent model contains an infinite family of fields which are labelled by different noncommutativity parameters, and related to each other by Lorentz transformations. The relative localization properties of these fields are investigated, and it is shown that to each field one can assign a wedge-shaped localization region of Minkowski space. This assignment is consistent with the principles of covariance and locality, i.e. fields localized in spacelike separated wedges commute. Regarding the model as a non-local, but wedge-local, quantum field theory on ordinary (commutative) Minkowski spacetime, it is possible to determine two-particle S-matrix elements, which turn out to be non-trivial. Some partial negative results concerning the existence of observables with sharper localization properties are also obtained.