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.
QED on the Groenewold Moyal Plane
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We investigate a version of noncommutative QED where the interaction term, although natural, breaks the spin-statistics connection. We calculate $e^- + e^- -> e^- + e^-$ and $\gamma + e^- -> \gamma + e^-$ cross-sections in the tree approximation and explicitly display their dependence on theta^{\mu \nu}. Remarkably the zero of the elastic $e^- + e^- -> e^- + e^-$ cross-section at 90-degrees in the center-of-mass system, which is due to Pauli principle, is shifted away as a function of theta^{\mu \nu} and energy.
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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.