Asymmetry in momentum space: restoring $\mathcal{C}\mathcal{P}\mathcal{T}$ invariance of $\kappa$-field theory

Abstract

The positive and negative energy modes of a field theory in $\kappa$-Minkowski/$\kappa$-Poincaré noncommutative spacetime have very different symmetry properties. This can be understood geometrically by considering that they span two distinct sectors of a curved momentum space. By performing an explicit direct computation of the relativistic Noether charges and their algebra within the canonical formalism, we identify a striking consequence of this asymmetry in momentum space: charge conjugation and Poincaré invariance are incompatible. We then notice how the structure of momentum space suggests that time reversal could be deformed so that the overall $\mathcal{C}\mathcal{P}\mathcal{T}$-invariance is restored. We prove that this new proposal works by studying the transformation properties under deformed discrete symmetries of the new relativistic charges.

V2 is the postprint version of the paper accepted for publication in Physical Review D 113, 026025 (2026). Several sections, including the abstract, have been rewritten to clarify some of the key results of the paper

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