  Gauge invariance of noncommutative (NC) regularization which, on the basis of
a Lorentz-invariant NC action regarded as a `regulated' action, neither
introduces auxiliary fields nor extends dimensions to complex values, is proved
by explicitly calculating photon self-energy in the one-loop approximation in
scalar QED. Transversality of vacuum polarization in NC regularization is also
briefly reviewed comparing with Pauli-Villars-Gupta and dimensional
regularizations. NC regularization is applied to gauge-invariant calculation of
one-loop gluon self-energy in U(N) gauge theory. It is shown that U(1)
decouples from SU(N) in the one-loop gluon self-energy diagrams. That is,
gauge-invariant result on the one-loop SU(N) gluon self-energy is obtained from
consideration of Lorentz-invariant NC U(N) gauge theory.
