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

• URL: http://arxiv.org/abs/2607.25833v2
• Date: Thu, 30 Jul 2026 18:35:48 GMT
• Title: Curved momentum space and finite Landau spectrum in $κ$-Minkowski spacetime
• Abstract summary: It is obtained the $$-Poincare Casimir from the de Sitter geometry of momentum space.<n>It is employed as the dynamical constraint governing charged particles within the framework of Poisson gauge theory.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It is obtained the $κ$-Poincare Casimir from the de Sitter geometry of momentum space and employed as the dynamical constraint governing charged particles within the framework of Poisson gauge theory. The resulting formalism is applied to investigate both scalar and spin-1/2 particles in a constant magnetic field. Exact energy spectra are obtained, including all orders in the deformation parameter $1/κ$. The curvature of momentum space implies a maximal invariant momentum, which in turn leads to a finite Landau spectrum characterized by the existence of a Highest Landau Level (HLL). In the fermionic case, the truncation becomes spin dependent, resulting in a polarized HLL. Possible implications of this ultraviolet truncation and its relation to anomaly-related phenomena are briefly discussed.

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