C, P, and T invariance of noncommutative gauge theories

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 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.