Towards new relativistic doubly $κ$-deformed D=4 quantum phase spaces
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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_ | 1866909617229922304 |
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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 new noncommutative models of quantum phase spaces, containing a pair of $κ$-deformed Poincaré algebras, with two independent double ($κ,\tildeκ$)-deformations in space-time and four-momenta sectors. The first such quantum phase space can be obtained by contractions $M,R\to \infty$ of recently introduced doubly $κ$-deformed $(κ,\tildeκ)$-Yang models, with the parameters $M,R$ describing inverse space-time and four-momenta curvatures and constant four-vectors $a_μ, b_μ$ determining nine types of $(κ,\tildeκ)$-deformations. The second considered model is provided by the nonlinear doubly $κ$-deformed TSR algebra spanned by 14 coset $\hat{o}(1,5)/\hat {o}(2)$ generators. The basic algebraic difference between the two models is the following: the first one, described by $\hat{o}(1,5)$ Lie algebra can be supplemented by the Hopf algebra structure, while the second model contains the quantum phase space commutators $[\hat{x}_μ,\hat{q}_ν]$, with the standard numerical $i\hbarη_{μν}$ term; therefore it describes the quantum-deformed Heisenberg algebra relations which cannot be equipped with the Hopf algebra. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_02339 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards new relativistic doubly $κ$-deformed D=4 quantum phase spaces Lukierski, Jerzy Meljanac, Stjepan Mignemi, Salvatore Pachoł, Anna Woronowicz, Mariusz High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics We propose new noncommutative models of quantum phase spaces, containing a pair of $κ$-deformed Poincaré algebras, with two independent double ($κ,\tildeκ$)-deformations in space-time and four-momenta sectors. The first such quantum phase space can be obtained by contractions $M,R\to \infty$ of recently introduced doubly $κ$-deformed $(κ,\tildeκ)$-Yang models, with the parameters $M,R$ describing inverse space-time and four-momenta curvatures and constant four-vectors $a_μ, b_μ$ determining nine types of $(κ,\tildeκ)$-deformations. The second considered model is provided by the nonlinear doubly $κ$-deformed TSR algebra spanned by 14 coset $\hat{o}(1,5)/\hat {o}(2)$ generators. The basic algebraic difference between the two models is the following: the first one, described by $\hat{o}(1,5)$ Lie algebra can be supplemented by the Hopf algebra structure, while the second model contains the quantum phase space commutators $[\hat{x}_μ,\hat{q}_ν]$, with the standard numerical $i\hbarη_{μν}$ term; therefore it describes the quantum-deformed Heisenberg algebra relations which cannot be equipped with the Hopf algebra. |
| title | Towards new relativistic doubly $κ$-deformed D=4 quantum phase spaces |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2410.02339 |