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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.15632 |
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| _version_ | 1866908890794295296 |
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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 |