Generalized Uncertainty Principle from the Regularized Self-Energy
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912109720240128 |
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| author | Jusufi, Kimet Ali, Ahmed Farag |
| author_facet | Jusufi, Kimet Ali, Ahmed Farag |
| contents | We use the Schrödinger--Newton equation to calculate the regularized self-energy of the particle using a regular self-gravitational and electrostatic potential derived in the string T-duality. The particle mass $M$ is no longer concentrated into a point but it is diluted and described by a quantum-corrected smeared energy density resulting in corrections to the energy of the particle which is interpreted as a regularized self-energy. We extend our results and find corrections to the relativistic particles using the Klein-Gordon, Proca, and Dirac equations. An important finding is that we extract a form of generalized uncertainty principle (GUP) from the corrected energy. The form of GUP is shown to depend on the nature of particles; namely, for bosons (spin $0$ and spin $1$) we obtain a quadratic form of GUP, while for fermions (spin $1/2$) we obtain a linear form of GUP. The correlation we found between spin and GUP may offer insights into investigating quantum gravity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_07198 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalized Uncertainty Principle from the Regularized Self-Energy Jusufi, Kimet Ali, Ahmed Farag High Energy Physics - Theory General Relativity and Quantum Cosmology We use the Schrödinger--Newton equation to calculate the regularized self-energy of the particle using a regular self-gravitational and electrostatic potential derived in the string T-duality. The particle mass $M$ is no longer concentrated into a point but it is diluted and described by a quantum-corrected smeared energy density resulting in corrections to the energy of the particle which is interpreted as a regularized self-energy. We extend our results and find corrections to the relativistic particles using the Klein-Gordon, Proca, and Dirac equations. An important finding is that we extract a form of generalized uncertainty principle (GUP) from the corrected energy. The form of GUP is shown to depend on the nature of particles; namely, for bosons (spin $0$ and spin $1$) we obtain a quadratic form of GUP, while for fermions (spin $1/2$) we obtain a linear form of GUP. The correlation we found between spin and GUP may offer insights into investigating quantum gravity. |
| title | Generalized Uncertainty Principle from the Regularized Self-Energy |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2303.07198 |