From Snyder space-times to doubly $κ$-dependent Yang quantum phase spaces and their generalizations
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913360417652736 |
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| author | Lukierski, Jerzy Meljanac, Stjepan Mignemi, Salvatore Pachoł, Anna Woronowicz, Mariusz |
| author_facet | Lukierski, Jerzy Meljanac, Stjepan Mignemi, Salvatore Pachoł, Anna Woronowicz, Mariusz |
| contents | We propose the doubly $κ$-dependent Yang quantum phase space which describes the generalization of $D = 4$ Yang model. We postulate that such model is covariant under the generalized Born map, what permits to derive this new model from the earlier proposed $κ$-Snyder model. Our model of $D=4$ relativistic Yang quantum phase space depends on five deformation parameters which form two Born map-related dimensionful pairs: $(M,R)$ specifying the standard Yang model and $(κ,\tildeκ)$ characterizing the Born-dual $κ$-dependence of quantum space-time and quantum fourmomenta sectors; fifth parameter $ρ$ is dimensionless and Born-selfdual. In the last section, we propose the Kaluza-Klein generalization of $D=4$ Yang model and the new quantum Yang models described algebraically by quantum-deformed $\hat{o}(1,5)$ algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_16994 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | From Snyder space-times to doubly $κ$-dependent Yang quantum phase spaces and their generalizations Lukierski, Jerzy Meljanac, Stjepan Mignemi, Salvatore Pachoł, Anna Woronowicz, Mariusz High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics We propose the doubly $κ$-dependent Yang quantum phase space which describes the generalization of $D = 4$ Yang model. We postulate that such model is covariant under the generalized Born map, what permits to derive this new model from the earlier proposed $κ$-Snyder model. Our model of $D=4$ relativistic Yang quantum phase space depends on five deformation parameters which form two Born map-related dimensionful pairs: $(M,R)$ specifying the standard Yang model and $(κ,\tildeκ)$ characterizing the Born-dual $κ$-dependence of quantum space-time and quantum fourmomenta sectors; fifth parameter $ρ$ is dimensionless and Born-selfdual. In the last section, we propose the Kaluza-Klein generalization of $D=4$ Yang model and the new quantum Yang models described algebraically by quantum-deformed $\hat{o}(1,5)$ algebras. |
| title | From Snyder space-times to doubly $κ$-dependent Yang quantum phase spaces and their generalizations |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2311.16994 |