Deformed algebraic structure of angular momenta: GUP perspective
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909407702417408 |
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| author | Bhandari, Gaurav Pathak, S. D. Sharma, Manabendra Wang, Anzhong |
| author_facet | Bhandari, Gaurav Pathak, S. D. Sharma, Manabendra Wang, Anzhong |
| contents | The prediction of a minimal length scale by various quantum gravity candidates (such as string/M theory, Doubly Special Relativity, Loop Quantum Gravity and others) have suggested modification of Heisenberg Uncertainty Principle (HUP), resulting in the Generalized Uncertainty Principle (GUP).
In this short review, we investigate the origins of the GUP and examine higher-order models, focusing on the linear plus quadratic form of the GUP. We extend the concept of minimal length to minimal angular resolution, which plays a crucial role in modifying angular momentum and its associated algebra. A comparison is made between the standard angular momentum commutator algebra and that modified by the GUP. Finally, we review its application in the hydrogen atom spectra and and discuss future endeavors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18901 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deformed algebraic structure of angular momenta: GUP perspective Bhandari, Gaurav Pathak, S. D. Sharma, Manabendra Wang, Anzhong General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Quantum Physics The prediction of a minimal length scale by various quantum gravity candidates (such as string/M theory, Doubly Special Relativity, Loop Quantum Gravity and others) have suggested modification of Heisenberg Uncertainty Principle (HUP), resulting in the Generalized Uncertainty Principle (GUP). In this short review, we investigate the origins of the GUP and examine higher-order models, focusing on the linear plus quadratic form of the GUP. We extend the concept of minimal length to minimal angular resolution, which plays a crucial role in modifying angular momentum and its associated algebra. A comparison is made between the standard angular momentum commutator algebra and that modified by the GUP. Finally, we review its application in the hydrogen atom spectra and and discuss future endeavors. |
| title | Deformed algebraic structure of angular momenta: GUP perspective |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2411.18901 |