Discrete Symmetries (C,P,T) in Noncommutative Field Theories

In this paper we study the invariance of the noncmmutative gauge theories under C, P and T transformations. For the noncommutative space (when only the spatial part of $\theta$ is non-zero) we show that NCQED is Parity invariant. In addition, we show that under charge conjugation the theory on noncommutative $R^4_{\theta}$ is transformed to the theory on $R^4_{-\theta}$, so NCQED is a 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 CPT invariant. Moreover we show that the CPT invariance holds for general noncommutative space-time.