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Main Authors: Boumali, Abdelmalek, Jafari, Nosratollah
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2603.15632
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author Boumali, Abdelmalek
Jafari, Nosratollah
author_facet Boumali, Abdelmalek
Jafari, Nosratollah
contents % Doubly Special Relativity (DSR) introduces, besides the invariant speed of light $c$, an observer-independent high-energy % scale that deforms relativistic kinematics and can be implemented through modified dispersion relations or effective % wave equations with energy-dependent spatial operators. In this work we develop a three-dimensional, exactly solvable % benchmark for such deformations in the spin-$\tfrac12$ sector: the Dirac oscillator. Following the original % construction of Moshinsky and Szczepaniak, the oscillator is introduced through a linear non-minimal momentum coupling, % which preserves Hermiticity and yields, after decoupling the Dirac equation into large and small components, a % three-dimensional isotropic harmonic-oscillator operator supplemented by a strong spin--orbit term. % We then incorporate Planck-scale deformations in two standard DSR realizations (Amelino--Camelia and % Magueijo--Smolin, characterized by an invariant energy scale $k$) and in a generalized DSR framework based on a % first-order expansion in the Planck length $l_p$. In all cases the bound-state eigenfunctions retain the % oscillator-spinor structure dictated by spherical symmetry, while DSR deforms the algebraic relation between quantum % numbers $(N,j,\ell)$ and the relativistic energy, producing branch-dependent shifts for both particle and antiparticle % solutions. The undeformed limit ($k\to\infty$ or $l_p\to0$) is recovered smoothly and the deformation signal increases % with excitation through the oscillator scale and spin--orbit splitting.
format Preprint
id arxiv_https___arxiv_org_abs_2603_15632
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Three-Dimensional Modified Dirac Oscillator in Standard and Generalized Doubly Special Relativity
Boumali, Abdelmalek
Jafari, Nosratollah
General Physics
High Energy Physics - Theory
% Doubly Special Relativity (DSR) introduces, besides the invariant speed of light $c$, an observer-independent high-energy % scale that deforms relativistic kinematics and can be implemented through modified dispersion relations or effective % wave equations with energy-dependent spatial operators. In this work we develop a three-dimensional, exactly solvable % benchmark for such deformations in the spin-$\tfrac12$ sector: the Dirac oscillator. Following the original % construction of Moshinsky and Szczepaniak, the oscillator is introduced through a linear non-minimal momentum coupling, % which preserves Hermiticity and yields, after decoupling the Dirac equation into large and small components, a % three-dimensional isotropic harmonic-oscillator operator supplemented by a strong spin--orbit term. % We then incorporate Planck-scale deformations in two standard DSR realizations (Amelino--Camelia and % Magueijo--Smolin, characterized by an invariant energy scale $k$) and in a generalized DSR framework based on a % first-order expansion in the Planck length $l_p$. In all cases the bound-state eigenfunctions retain the % oscillator-spinor structure dictated by spherical symmetry, while DSR deforms the algebraic relation between quantum % numbers $(N,j,\ell)$ and the relativistic energy, producing branch-dependent shifts for both particle and antiparticle % solutions. The undeformed limit ($k\to\infty$ or $l_p\to0$) is recovered smoothly and the deformation signal increases % with excitation through the oscillator scale and spin--orbit splitting.
title Three-Dimensional Modified Dirac Oscillator in Standard and Generalized Doubly Special Relativity
topic General Physics
High Energy Physics - Theory
url https://arxiv.org/abs/2603.15632