Generalized quantum phase spaces for the κ-deformed extended Snyder model
We describe, in an algebraic way, the κ-deformed extended Snyder models, that depend on three parameters β,κ and λ, which in a suitable algebra basis are described by the de Sitter algebras o(1,N). The commutation relations of the algebra contain a parameter λ, which is used for the calculations of...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-03-01
|
| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269323000436 |
| _version_ | 1797905320293433344 |
|---|---|
| author | Jerzy Lukierski Stjepan Meljanac Salvatore Mignemi Anna Pachoł |
| author_facet | Jerzy Lukierski Stjepan Meljanac Salvatore Mignemi Anna Pachoł |
| author_sort | Jerzy Lukierski |
| collection | DOAJ |
| description | We describe, in an algebraic way, the κ-deformed extended Snyder models, that depend on three parameters β,κ and λ, which in a suitable algebra basis are described by the de Sitter algebras o(1,N). The commutation relations of the algebra contain a parameter λ, which is used for the calculations of perturbative expansions. For such κ-deformed extended Snyder models we consider the Heisenberg double with dual generalized momenta sector, and provide the respective generalized quantum phase space depending on three parameters mentioned above. Further, we study for these models an alternative Heisenberg double, with the algebra of functions on de Sitter group. In both cases we calculate the formulae for the cross commutation relations between generalized coordinate and momenta sectors, at linear order in λ. We demonstrate that in the commutators of quantum space-time coordinates and momenta of the quantum-deformed Heisenberg algebra the terms generated by κ-deformation are dominating over β-dependent ones for small values of λ. |
| first_indexed | 2024-04-10T10:03:37Z |
| format | Article |
| id | doaj.art-4e0a91f1a7b344da8cdfb7764d268a74 |
| institution | Directory Open Access Journal |
| issn | 0370-2693 |
| language | English |
| last_indexed | 2024-04-10T10:03:37Z |
| publishDate | 2023-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-4e0a91f1a7b344da8cdfb7764d268a742023-02-16T04:17:41ZengElsevierPhysics Letters B0370-26932023-03-01838137709Generalized quantum phase spaces for the κ-deformed extended Snyder modelJerzy Lukierski0Stjepan Meljanac1Salvatore Mignemi2Anna Pachoł3Institute of Theoretical Physics, Wrocław University, pl. Maxa Borna 9, 50-205 Wrocław, PolandDivision of Theoretical Physics, Rudjer Bošković Institute, Bijenička c.54, HR-10002 Zagreb, CroatiaDipartimento di Matematica, Università di Cagliari, via Ospedale 72, 09124 Cagliari, Italy; INFN, Sezione di Cagliari, 09042 Monserrato, Italy; Corresponding author.Department of Microsystems, University of South-Eastern Norway, Campus Vestfold, Raveien 215, 3184 Borre, NorwayWe describe, in an algebraic way, the κ-deformed extended Snyder models, that depend on three parameters β,κ and λ, which in a suitable algebra basis are described by the de Sitter algebras o(1,N). The commutation relations of the algebra contain a parameter λ, which is used for the calculations of perturbative expansions. For such κ-deformed extended Snyder models we consider the Heisenberg double with dual generalized momenta sector, and provide the respective generalized quantum phase space depending on three parameters mentioned above. Further, we study for these models an alternative Heisenberg double, with the algebra of functions on de Sitter group. In both cases we calculate the formulae for the cross commutation relations between generalized coordinate and momenta sectors, at linear order in λ. We demonstrate that in the commutators of quantum space-time coordinates and momenta of the quantum-deformed Heisenberg algebra the terms generated by κ-deformation are dominating over β-dependent ones for small values of λ.http://www.sciencedirect.com/science/article/pii/S0370269323000436 |
| spellingShingle | Jerzy Lukierski Stjepan Meljanac Salvatore Mignemi Anna Pachoł Generalized quantum phase spaces for the κ-deformed extended Snyder model Physics Letters B |
| title | Generalized quantum phase spaces for the κ-deformed extended Snyder model |
| title_full | Generalized quantum phase spaces for the κ-deformed extended Snyder model |
| title_fullStr | Generalized quantum phase spaces for the κ-deformed extended Snyder model |
| title_full_unstemmed | Generalized quantum phase spaces for the κ-deformed extended Snyder model |
| title_short | Generalized quantum phase spaces for the κ-deformed extended Snyder model |
| title_sort | generalized quantum phase spaces for the κ deformed extended snyder model |
| url | http://www.sciencedirect.com/science/article/pii/S0370269323000436 |
| work_keys_str_mv | AT jerzylukierski generalizedquantumphasespacesforthekdeformedextendedsnydermodel AT stjepanmeljanac generalizedquantumphasespacesforthekdeformedextendedsnydermodel AT salvatoremignemi generalizedquantumphasespacesforthekdeformedextendedsnydermodel AT annapachoł generalizedquantumphasespacesforthekdeformedextendedsnydermodel |