Discrete Symmetries In Lorentz-Invariant Non-Commutative QED

Abstract

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