Dirac Oscillator in DSR: A Comparative Study of Magueijo-Smolin and Amelino-Camelia Models
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911195011743744 |
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| author | Jafari, Nosratollah Boumali, Abdelmalek |
| author_facet | Jafari, Nosratollah Boumali, Abdelmalek |
| contents | This paper investigates the energy spectrum of the Dirac oscillator within the framework of Doubly Special Relativity (DSR), focusing on two prominent models: the Magueijo--Smolin (MS) and Amelino-Camelia models. We derive the modified Dirac equations in both MS and Amelino-Camelia DSR models under the approximation of $$O(E^{2}/k^{2})$$ for a single particle and examine the resulting energy spectra. The study reveals significant corrections to the standard relativistic Dirac oscillator spectrum due to the Planck-scale deformation parameter $$k$$, which introduces distinct deviations depending on the DSR model employed. For the MS model, we observe non-uniform shifts in both positive and negative energy branches at small $$k$$, with the spectrum gradually flattening toward the canonical result as $$k$$ increases. In the Amelino-Camelia model, the energy levels show larger deviations at lower values of $$k$$, and these anomalies diminish more slowly compared to the MS model. The results provide insights into the impact of quantum gravity effects on quantum systems, with potential applications in high-precision spectroscopic or astrophysical observations at energies near the Planck scale. Furthermore, the comparative analysis of these two DSR models highlights the robustness of Planck-scale predictions and guides future experimental efforts aimed at detecting quantum-gravity signatures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05117 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dirac Oscillator in DSR: A Comparative Study of Magueijo-Smolin and Amelino-Camelia Models Jafari, Nosratollah Boumali, Abdelmalek General Physics This paper investigates the energy spectrum of the Dirac oscillator within the framework of Doubly Special Relativity (DSR), focusing on two prominent models: the Magueijo--Smolin (MS) and Amelino-Camelia models. We derive the modified Dirac equations in both MS and Amelino-Camelia DSR models under the approximation of $$O(E^{2}/k^{2})$$ for a single particle and examine the resulting energy spectra. The study reveals significant corrections to the standard relativistic Dirac oscillator spectrum due to the Planck-scale deformation parameter $$k$$, which introduces distinct deviations depending on the DSR model employed. For the MS model, we observe non-uniform shifts in both positive and negative energy branches at small $$k$$, with the spectrum gradually flattening toward the canonical result as $$k$$ increases. In the Amelino-Camelia model, the energy levels show larger deviations at lower values of $$k$$, and these anomalies diminish more slowly compared to the MS model. The results provide insights into the impact of quantum gravity effects on quantum systems, with potential applications in high-precision spectroscopic or astrophysical observations at energies near the Planck scale. Furthermore, the comparative analysis of these two DSR models highlights the robustness of Planck-scale predictions and guides future experimental efforts aimed at detecting quantum-gravity signatures. |
| title | Dirac Oscillator in DSR: A Comparative Study of Magueijo-Smolin and Amelino-Camelia Models |
| topic | General Physics |
| url | https://arxiv.org/abs/2510.05117 |