C,P, andTInvariance of Noncommutative Gauge Theories

Abstract

In this paper we study the invariance of the noncommutative gauge theories under $C$, $P$, and $T$ transformations. For the noncommutative space (when only the spatial part of $\theta$ is nonzero) we show that noncommutative QED (NCQED) is parity invariant. In addition, we show that under charge conjugation the theory on noncommutative $R_{\theta }^4$ is transformed to the theory on $R_{-\theta }^4$, so NCQED is a $\mathrm{CP}$ violating theory. The theory remains invariant under time reversal if, together with proper changes in fields, we also change $\theta$ by $-\theta$. Hence altogether NCQED is $\mathrm{CPT}$ invariant. Moreover, we show that the $\mathrm{CPT}$ invariance holds for general noncommutative space-time.