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

Abstract

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 $θ$ is non-zero) we show that NCQED is Parity invariant. In addition, we show that under charge conjugation the theory on noncommutative $R^4_θ$ is transformed to the theory on $R^4_{-θ}$, so NCQED is a CP violating theory. The theory remains invariant under time reversal if, together with proper changes in fields, we also change $θ$ by $-θ$. Hence altogether NCQED is CPT invariant. Moreover we show that the CPT invariance holds for general noncommutative space-time.