S-Matrix on the Moyal Plane: Locality versus Lorentz Invariance

TL;DR

This paper investigates the causality and Lorentz invariance of quantum field theories on the Moyal plane, revealing that matter interactions with non-abelian gauge fields violate these fundamental principles.

Contribution

It demonstrates that matter-only and matter with U(1) gauge interactions are causal, while non-abelian gauge interactions break causality and Lorentz invariance in twisted quantum field theories.

Findings

Matter-only and matter-U(1) interactions are causal.

Matter-non-abelian gauge interactions violate causality.

Interactions with non-abelian gauge fields are not Lorentz- and CPT-invariant.

Abstract

Twisted quantum field theories on the Groenewold-Moyal plane are known to be non-local. Despite this non-locality, it is possible to define a generalized notion of causality. We show that interacting quantum field theories that involve only couplings between matter fields, or between matter fields and minimally coupled U(1) gauge fields are causal in this sense. On the other hand, interactions between matter fields and non-abelian gauge fields violate this generalized causality. We derive the modified Feynman rules emergent from these features. They imply that interactions of matter with non-abelian gauge fields are not Lorentz- and CPT-invariant.