Abstract
Main properties of noncommutative (NC) gauge theory are investigated in a two-dimensional twisted Moyal plane, generated by vector fields Xa = eμa(x)∂μ; the dynamical effects are induced by a nontrivial tensor eμa(x). Connections in such a NC space are defined. Symmetry analysis is performed and related NC action is proved to be invariant under defined NC gauge transformations. A locally conserved Noether current is explicitly computed. Both commuting and noncommutative vector fields Xa are considered.
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