A non-geometric bootstrap on the Moyal plane produces noncommutative gauge theories and derives the U(N) fundamental restriction from the requirement that the conserved non-local current be Lie algebra valued.
S-Matrix on the Moyal Plane: Locality versus Lorentz Invariance
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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.
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On a non-geometric approach to noncommutative gauge theories
A non-geometric bootstrap on the Moyal plane produces noncommutative gauge theories and derives the U(N) fundamental restriction from the requirement that the conserved non-local current be Lie algebra valued.