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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2602.09861 |
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| _version_ | 1866912894543724544 |
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| author | Jafari, N. Boumali, A. |
| author_facet | Jafari, N. Boumali, A. |
| contents | We study the $(1+1)$-dimensional Dirac oscillator within a class of doubly special relativity (DSR) models generated by linear-fractional (projective) transformations on momentum space that preserve both the invariant speed of light and a high-energy observer-independent scale $\Ep$. Starting from the associated deformed Casimir invariants, we construct the coordinate-space Dirac equations for three inequivalent choices of the deformation vector (time-like, space-like, and light-like). For the time-like and light-like realizations the deformation induces momentum-dependent effective mass operators, which makes the coordinate-space formulation sensitive to operator ordering. To retain locality and obtain solvable second-order equations we adopt a reverted-product ordering prescription. Closed-form relativistic energy spectra and eigenfunctions are obtained in all three geometries, and the standard Dirac-oscillator results are recovered smoothly in the limit $\Ep\to\infty$. Finally, we derive the nonrelativistic expansion of the positive-energy branch and show that the deformation geometry controls the leading rest-energy shift and the renormalization of the oscillator level spacing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09861 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Deformed Dirac Oscillator in Linear-Fractional Doubly Special Relativity Jafari, N. Boumali, A. High Energy Physics - Theory We study the $(1+1)$-dimensional Dirac oscillator within a class of doubly special relativity (DSR) models generated by linear-fractional (projective) transformations on momentum space that preserve both the invariant speed of light and a high-energy observer-independent scale $\Ep$. Starting from the associated deformed Casimir invariants, we construct the coordinate-space Dirac equations for three inequivalent choices of the deformation vector (time-like, space-like, and light-like). For the time-like and light-like realizations the deformation induces momentum-dependent effective mass operators, which makes the coordinate-space formulation sensitive to operator ordering. To retain locality and obtain solvable second-order equations we adopt a reverted-product ordering prescription. Closed-form relativistic energy spectra and eigenfunctions are obtained in all three geometries, and the standard Dirac-oscillator results are recovered smoothly in the limit $\Ep\to\infty$. Finally, we derive the nonrelativistic expansion of the positive-energy branch and show that the deformation geometry controls the leading rest-energy shift and the renormalization of the oscillator level spacing. |
| title | The Deformed Dirac Oscillator in Linear-Fractional Doubly Special Relativity |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.09861 |