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PreprintCC BY 4.0arXiv

Curved momentum space and finite Landau spectrum in κ-Minkowski spacetime

  • Adrián Huamán Vargas
  • Vladislav Kupriyanov
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Abstract

We derive the κ-Poincaré Casimir from the de Sitter geometry of momentum space and employ it as the dynamical constraint governing charged particles within the framework of Poisson gauge theory. The resulting formalism is applied to scalar and spin-1/2 particles in a constant magnetic field. Within the semiclassical Poisson-gauge framework, exact energy spectra are obtained without expanding in the deformation parameter 1/κ. On the positive-energy branch in bicrossproduct momentum coordinates, identifying these coordinates with the physical momenta entering the gauge coupling imposes an upper bound on their spatial magnitude. This bound leads to a finite number of admissible Landau-level indices and hence to a Highest Landau Level (HLL). In the fermionic case, the truncation is spin dependent for the factorization adopted here, resulting in a polarized HLL. Possible implications of this ultraviolet truncation and the limitations of the framework are briefly discussed.

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Cite

BibTeXRIS
BibTeX
@misc{vargas2026curved,
  title = {{Curved momentum space and finite Landau spectrum in $κ$-Minkowski spacetime}},
  author = {Adrián Huamán Vargas and Vladislav Kupriyanov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.25833},
  eprint = {2607.25833},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.25833},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Curved momentum space and finite Landau spectrum in κ-Minkowski spacetime
AU  - Adrián Huamán Vargas
AU  - Vladislav Kupriyanov
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2607.25833
UR  - https://arxiv.org/abs/2607.25833
AB  - We derive the κ-Poincaré Casimir from the de Sitter geometry of momentum space and employ it as the dynamical constraint governing charged particles within the framework of Poisson gauge theory. The resulting formalism is applied to scalar and spin-1/2 particles in a constant magnetic field. Within the semiclassical Poisson-gauge framework, exact energy spectra are obtained without expanding in the deformation parameter 1/κ. On the positive-energy branch in bicrossproduct momentum coordinates, identifying these coordinates with the physical momenta entering the gauge coupling imposes an upper bound on their spatial magnitude. This bound leads to a finite number of admissible Landau-level indices and hence to a Highest Landau Level (HLL). In the fermionic case, the truncation is spin dependent for the factorization adopted here, resulting in a polarized HLL. Possible implications of this ultraviolet truncation and the limitations of the framework are briefly discussed.
ER  -