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

TL;DR

This paper investigates the invariance properties of noncommutative gauge theories under discrete symmetries C, P, and T, revealing conditions under which NCQED preserves or violates these symmetries, and establishing CPT invariance generally.

Contribution

It provides a detailed analysis of discrete symmetry transformations in noncommutative gauge theories, including conditions for invariance and violation, and proves CPT invariance in general noncommutative space-time.

Findings

NCQED is parity invariant when only spatial noncommutativity is present.

Charge conjugation transforms NCQED on $R^4_{ heta}$ to $R^4_{- heta}$, indicating CP violation.

NCQED remains invariant under time reversal if $ heta$ is also reversed.

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 $\theta$ 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.