Parity-deformed $sl(2,R)$, $su(2)$ and $so(3)$ Algebras: a Basis for Quantum Optics and Quantum Communications Applications
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909617683955712 |
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| author | Chung, W. S. Hassanabadi, H. Nieto, L. M. Zarrinkamar, S. |
| author_facet | Chung, W. S. Hassanabadi, H. Nieto, L. M. Zarrinkamar, S. |
| contents | Having in mind the significance of parity (reflection) in various areas of physics, the single-mode and two-mode Wigner algebras are considered adding to them a reflection operator. The associated deformed $sl(2, R)$ algebra, $sl_ν(2,R)$ and the deformed $so(3)$ algebra, $so_ν(3)$, are constructed for the widely used Jordan-Schwinger and Holstein-Primakoff realizations, commenting on various aspects and ingredients of the formalism for both single-mode and two-mode cases. Finally, due to its potential application in the study of qubit and qutrit systems, the parity-deformed $so_ν(3)$ representation is analyzed based on the isomorphy of $so(3)$ and $su(2)$. Related applications are discussed as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12157 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parity-deformed $sl(2,R)$, $su(2)$ and $so(3)$ Algebras: a Basis for Quantum Optics and Quantum Communications Applications Chung, W. S. Hassanabadi, H. Nieto, L. M. Zarrinkamar, S. Mathematical Physics Quantum Physics Having in mind the significance of parity (reflection) in various areas of physics, the single-mode and two-mode Wigner algebras are considered adding to them a reflection operator. The associated deformed $sl(2, R)$ algebra, $sl_ν(2,R)$ and the deformed $so(3)$ algebra, $so_ν(3)$, are constructed for the widely used Jordan-Schwinger and Holstein-Primakoff realizations, commenting on various aspects and ingredients of the formalism for both single-mode and two-mode cases. Finally, due to its potential application in the study of qubit and qutrit systems, the parity-deformed $so_ν(3)$ representation is analyzed based on the isomorphy of $so(3)$ and $su(2)$. Related applications are discussed as well. |
| title | Parity-deformed $sl(2,R)$, $su(2)$ and $so(3)$ Algebras: a Basis for Quantum Optics and Quantum Communications Applications |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2407.12157 |