  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.
