Discrete Symmetries In Lorentz-Invariant Non-Commutative QED

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 $\htheta^{μν}$, is $C$-, $P$- and $T$-invariant. It is then proved that $C,P$ and $T$ are separately conserved in Lorentz-invariant Non-Commutative QED.

19pages

References in corpus (3)

• General Properties of Noncommutative Field Theories
• Ultraviolet Finite Quantum Field Theory on Quantum Spacetime
• Lorentz-Invariant Non-Commutative QED

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• Aspects of noncommutativity in field theory, strings and membranes