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Asymmetry in momentum space: Restoring CPT invariance of κ-field theory

Tadeusz Adach1, Andrea Bevilacqua2, Jerzy Kowalski-Glikman2,1, and Giacomo Rosati3,4

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Phys. Rev. D 113, 026025 – Published 28 January, 2026

DOI: https://doi.org/10.1103/7qy4-fb7f

Abstract

The positive and negative energy modes of a field theory in κ-Minkowski/κ-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 CPT-invariance is restored. We prove that this new proposal works by studying the transformation properties under deformed discrete symmetries of the new relativistic charges.

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Phys. Rev. D 113, 026025– Published 28 January, 2026
  • Received 5 August 2025
  • Accepted 9 January 2026
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