Computing noncommutative Chern-Simons theory radiative corrections on the back of an envelope

We show that the renormalized U(N) noncommutative. Chem-Simons theory can b e defined in perturbation theory so that there are no loop corrections to t he IPI functional of the theory in an arbitrary homogeneous axial (time-lik e, light-like or space-like) gauge. We define the free propagators of the f ields of the theory by using the Leibbrandt-Mandelstam prescription which a llows Wick rotation and is consistent with power-counting - and regularize its Green functions with the help of a family of regulators which explicitl y preserve the infinitesimal vector Grassmann symmetry of the theory. We al so show that in perturbation theory the nonvanishing Green functions of the elementary fields of the theory are products of the free propagators. (C) 2001 Elsevier Science BN. All rights reserved.