Asymmetry in momentum space: restoring ${\cal C}{\cal P}{\cal T}$ invariance of $κ$-field theory
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908799382585344 |
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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 |