Two-body Dirac equation in DSR: results for fermion-antifermion pairs
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917069126107136 |
|---|---|
| author | Jafari, Nosratollah Guvendi, Abdullah |
| author_facet | Jafari, Nosratollah Guvendi, Abdullah |
| contents | This study investigates a modified two-body Dirac equation in (2+1)-dimensional spacetime, inspired by Amelino-Camelia's doubly special relativity (DSR). We begin by deriving a covariant two-body Dirac equation that, in the absence of DSR modifications, reduces to a Bessel-type wave equation. Incorporating corrections from the chosen DSR model modifies this wave equation, yielding solutions consistent with established results in the low-energy regime. We demonstrate that the effects of DSR modifications become particularly pronounced at large relative distances. For a coupled fermion-antifermion pair, we derive the modified binding energy solutions. By accounting for first-order Planck-scale corrections, we show that the fine-structure constant αbehaves as an energy-dependent running parameter, given by \(α_{eff(E)}/α\approx 1 - \frac{E}{4E_p}\), where E_p is the Planck energy. Binding energy levels are computed using a first-order approximation of the DSR modifications, and the results are applied to positronium-like systems. Our model reveals that DSR modifications induce shifts in the binding energy levels. To the best of our knowledge, DSR-modified two-body equations have not been previously studied. This model is the first of its kind, opening new avenues for further research in this area. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05641 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-body Dirac equation in DSR: results for fermion-antifermion pairs Jafari, Nosratollah Guvendi, Abdullah General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory This study investigates a modified two-body Dirac equation in (2+1)-dimensional spacetime, inspired by Amelino-Camelia's doubly special relativity (DSR). We begin by deriving a covariant two-body Dirac equation that, in the absence of DSR modifications, reduces to a Bessel-type wave equation. Incorporating corrections from the chosen DSR model modifies this wave equation, yielding solutions consistent with established results in the low-energy regime. We demonstrate that the effects of DSR modifications become particularly pronounced at large relative distances. For a coupled fermion-antifermion pair, we derive the modified binding energy solutions. By accounting for first-order Planck-scale corrections, we show that the fine-structure constant αbehaves as an energy-dependent running parameter, given by \(α_{eff(E)}/α\approx 1 - \frac{E}{4E_p}\), where E_p is the Planck energy. Binding energy levels are computed using a first-order approximation of the DSR modifications, and the results are applied to positronium-like systems. Our model reveals that DSR modifications induce shifts in the binding energy levels. To the best of our knowledge, DSR-modified two-body equations have not been previously studied. This model is the first of its kind, opening new avenues for further research in this area. |
| title | Two-body Dirac equation in DSR: results for fermion-antifermion pairs |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.05641 |