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

Understand

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.