The BRS invariance of noncommutative Yang–Mills theory at the one-loop level

Abstract

We show that U(N) Yang-Mills theory on noncommutative Minkowski space-time can be renormalized, in a BRS invariant way, at the one-loop level, by multiplicative dimensional renormalization of its coupling constant, its gauge parameter and its fields. It is shown that the Slavnov-Taylor equation, the gauge-fixing equation and the ghost equation hold, up to order $\hbar$, for the MS renormalized noncommutative U(N) Yang-Mills theory. We give the value of the pole part of every 1PI diagram which is UV divergent.