Discrete Symmetries In Lorentz-Invariant Non-Commutative QED

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