Twisted Yang-Mills field theory: connections and Noether current

Main properties of noncommutative (NC) gauge theory are investigated in a $2-$dimensional twisted Moyal plane, generated by vector fields $X_{a}=e_{a}^μ(x)\partial_μ;$ the dynamical effects are induced by a non trivial tensor $e_{a}^μ(x)$. 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 $X_{a}$ are considered.

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