Doubly $κ$-deformed Yang models, Born-selfdual $κ$-deformed quantum phase spaces and two generalizations of Yang models
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913460325974016 |
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| author | Lukierski, Jerzy Pachoł, Anna |
| author_facet | Lukierski, Jerzy Pachoł, Anna |
| contents | Recently it was shown that by using two different realizations of $\hat{o}(1,4)$ Lie algebra one can describe one-parameter standard Snyder model and two-parameter $κ$-deformed Snyder model. In this paper, by using the generalized Born duality and Jacobi identities we obtain from the $κ$-deformed Snyder model the doubly $κ$-deformed Yang model which provides the new class of quantum relativistic phase spaces. These phase spaces contain as subalgebras the $κ$-deformed Minkowski space-time as well as quantum $\tildeκ$-deformed fourmomenta and are depending on five independent parameters. Such a large class of quantum phase spaces can be described in $D=4$ by particular realizations of $\hat{o}(1,5)$ algebra, what illustrates the property that in noncommutative geometry different $D=4$ physical models may be described by various realizations of the same algebraic structure. Finally, in the last Section we propose two new ways of generalizing Yang models: by introducing $\hat o(1,3+2N)$ algebras ($N=1,2\ldots$) we provide internal symmetries $O(N)$ symmetries in Kaluza-Klein extended Yang model, and by replacing the classical $\hat{o}(1,5)$ algebras which describe the algebraic structure of Yang models by $\hat o(1,5)$ quantum groups with suitably chosen nonprimitive coproducts. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_16497 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Doubly $κ$-deformed Yang models, Born-selfdual $κ$-deformed quantum phase spaces and two generalizations of Yang models Lukierski, Jerzy Pachoł, Anna High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Recently it was shown that by using two different realizations of $\hat{o}(1,4)$ Lie algebra one can describe one-parameter standard Snyder model and two-parameter $κ$-deformed Snyder model. In this paper, by using the generalized Born duality and Jacobi identities we obtain from the $κ$-deformed Snyder model the doubly $κ$-deformed Yang model which provides the new class of quantum relativistic phase spaces. These phase spaces contain as subalgebras the $κ$-deformed Minkowski space-time as well as quantum $\tildeκ$-deformed fourmomenta and are depending on five independent parameters. Such a large class of quantum phase spaces can be described in $D=4$ by particular realizations of $\hat{o}(1,5)$ algebra, what illustrates the property that in noncommutative geometry different $D=4$ physical models may be described by various realizations of the same algebraic structure. Finally, in the last Section we propose two new ways of generalizing Yang models: by introducing $\hat o(1,3+2N)$ algebras ($N=1,2\ldots$) we provide internal symmetries $O(N)$ symmetries in Kaluza-Klein extended Yang model, and by replacing the classical $\hat{o}(1,5)$ algebras which describe the algebraic structure of Yang models by $\hat o(1,5)$ quantum groups with suitably chosen nonprimitive coproducts. |
| title | Doubly $κ$-deformed Yang models, Born-selfdual $κ$-deformed quantum phase spaces and two generalizations of Yang models |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2405.16497 |