Discrete Symmetries In Lorentz-Invariant Non-Commutative QED

TL;DR

This paper discusses how Lorentz-invariant non-commutative QED maintains discrete symmetries like C, P, and T by using a covariant algebra with tensor operators, contrasting with traditional approaches that break these symmetries.

Contribution

It demonstrates that Lorentz-invariant non-commutative QED preserves C, P, and T symmetries by employing the DFR algebra with tensor operators, unlike standard non-commutative models.

Findings

C, P, and T are separately conserved in Lorentz-invariant NCQED

The DFR algebra restores discrete symmetries in non-commutative gauge theories

Traditional $ heta$-algebra breaks P and T invariance unless formally transformed

Abstract

It is pointed out that the usual $\theta$-algebra assumed for non-commuting coordinates is not $P$- and $T$-invariant, unless one {\it formally} transforms the non-commutativity parameter $\theta^{\mu\nu}$ in an appropriate way. On the other hand, the Lorentz-covariant DFR algebra, which `relativitizes' the $\theta$-algebra by replacing $\theta^{\mu\nu}$ with a second-rank antisymmetric tensor operator $\htheta^{\mu\nu}$, is $C$-, $ P$- and $T$-invariant. It is then proved that $C, P$ and $T$ are separately conserved in Lorentz-invariant Non-Commutative QED.