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One-Particle Equivalence of Lorentz-Violating and Lorentz-Deformed Theories

  • Arshid Shabir
  • Francesco Marino
  • Mir Faizal
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Abstract

Planck-scale departures from special relativity are commonly described by theories that break Lorentz symmetry and theories in which such symmetry is deformed. We prove that, under a global shell-linearizability condition, these two descriptions are physically equivalent for a single particle, corresponding to unitarily equivalent realizations of the same Wigner orbit expressed in different momentum coordinates. This equivalence breaks down for multiparticle systems, except when the momentum-composition law can be reduced to the ordinary addition of momenta. Our results imply that the distinction between Lorentz violating and Lorentz-deformed kinematics can only be tested by genuine multiparticle observables. We discuss Compton edge measurements as a prototype example of such a multiparticle probe.

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Cite

BibTeXRIS
BibTeX
@misc{shabir2026oneparticle,
  title = {{One-Particle Equivalence of Lorentz-Violating and Lorentz-Deformed Theories}},
  author = {Arshid Shabir and Francesco Marino and Mir Faizal},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.09986},
  eprint = {2611.09986},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.09986},
}
RIS
TY  - UNPB
TI  - One-Particle Equivalence of Lorentz-Violating and Lorentz-Deformed Theories
AU  - Arshid Shabir
AU  - Francesco Marino
AU  - Mir Faizal
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.09986
UR  - https://arxiv.org/abs/2611.09986
AB  - Planck-scale departures from special relativity are commonly described by theories that break Lorentz symmetry and theories in which such symmetry is deformed. We prove that, under a global shell-linearizability condition, these two descriptions are physically equivalent for a single particle, corresponding to unitarily equivalent realizations of the same Wigner orbit expressed in different momentum coordinates. This equivalence breaks down for multiparticle systems, except when the momentum-composition law can be reduced to the ordinary addition of momenta. Our results imply that the distinction between Lorentz violating and Lorentz-deformed kinematics can only be tested by genuine multiparticle observables. We discuss Compton edge measurements as a prototype example of such a multiparticle probe.
ER  -