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

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Main Authors: Adach, Tadeusz, Bevilacqua, Andrea, Kowalski-Glikman, Jerzy, Rosati, Giacomo
Format: Preprint
Published: 2025
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author Adach, Tadeusz
Bevilacqua, Andrea
Kowalski-Glikman, Jerzy
Rosati, Giacomo
author_facet Adach, Tadeusz
Bevilacqua, Andrea
Kowalski-Glikman, Jerzy
Rosati, Giacomo
contents 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 ${\cal C}{\cal P}{\cal T}$-invariance is restored. We prove that this new proposal works by studying the transformation properties under deformed discrete symmetries of the new relativistic charges.
format Preprint
id arxiv_https___arxiv_org_abs_2507_16187
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Asymmetry in momentum space: restoring ${\cal C}{\cal P}{\cal T}$ invariance of $κ$-field theory
Adach, Tadeusz
Bevilacqua, Andrea
Kowalski-Glikman, Jerzy
Rosati, Giacomo
High Energy Physics - Theory
General Relativity and Quantum Cosmology
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 ${\cal C}{\cal P}{\cal T}$-invariance is restored. We prove that this new proposal works by studying the transformation properties under deformed discrete symmetries of the new relativistic charges.
title Asymmetry in momentum space: restoring ${\cal C}{\cal P}{\cal T}$ invariance of $κ$-field theory
topic High Energy Physics - Theory
General Relativity and Quantum Cosmology
url https://arxiv.org/abs/2507.16187