Abstract
Research progress on the noncommutative gauge theories on the Moyal space is discussed in this minireview. We first present a brief overview on the development of gauge theories on Moyal space, with an emphasis on the role of Seiberg–Witten maps. Two important relations induced by reversible Seiberg–Witten maps, namely the formal equivalence of the on-shell DeWitt background field effective action in general and the explicit identical relation between tree-level scattering amplitudes in noncommutative quantum electrodynamics (NCQED), are described in some detail. We then proceed to the properties of the tree-level two-by-two scattering amplitudes in NCQED, including a forward scattering singularity in NCQED Compton scattering. After covering some phenomenological perspectives of noncommutative Yang–Mills (NCYM)-based models, outlooks for the future are given at the end.
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