  We derive maps relating the currents and energy-momentum tensors in
noncommutative (NC) gauge theories with their commutative equivalents. Some
uses of these maps are discussed. Especially, in NC electrodynamics, we obtain
a generalization of the Lorentz force law. Also, the same map for anomalous
currents relates the Adler-Bell-Jackiw type NC covariant anomaly with the
standard commutative-theory anomaly. For the particular case of two dimensions,
we discuss the implications of these maps for the Sugawara-type energy-momentum
tensor.
