Twisted Yang-Mills field theory: connections and Noether current
Abstract
Main properties of noncommutative (NC) gauge theory are investigated in a
2−
dimensional twisted Moyal plane, generated by vector fields
X
a
=
e
μ
a
(x)
∂
μ
;
the dynamical effects are induced by a non trivial tensor
e
μ
a
(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.