Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups
The κ-deformation of the (2 + 1)D anti-de Sitter, Poincaré, and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter. The Drinfel’d-double and the Poisson–Lie structure underlying the κ-...
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Wiley
2017-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/7876942 |
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| author | Ángel Ballesteros N. Rossano Bruno Francisco J. Herranz |
| author_facet | Ángel Ballesteros N. Rossano Bruno Francisco J. Herranz |
| author_sort | Ángel Ballesteros |
| collection | DOAJ |
| description | The κ-deformation of the (2 + 1)D anti-de Sitter, Poincaré, and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter. The Drinfel’d-double and the Poisson–Lie structure underlying the κ-deformation are explicitly given, and the three quantum kinematical groups are obtained as quantizations of such Poisson–Lie algebras. As a consequence, the noncommutative (2 + 1)D spacetimes that generalize the κ-Minkowski space to the (anti-)de Sitter ones are obtained. Moreover, noncommutative 4D spaces of (time-like) geodesics can be defined, and they can be interpreted as a novel possibility to introduce noncommutative worldlines. Furthermore, quantum (anti-)de Sitter algebras are presented both in the known basis related to 2 + 1 quantum gravity and in a new one which generalizes the bicrossproduct one. In this framework, the quantum deformation parameter is related to the Planck length, and the existence of a kind of “duality” between the cosmological constant and the Planck scale is also envisaged. |
| format | Article |
| id | doaj-art-4105f27b17ad45bcaa41b2de6213ed24 |
| institution | Kabale University |
| issn | 1687-7357 1687-7365 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in High Energy Physics |
| spelling | doaj-art-4105f27b17ad45bcaa41b2de6213ed242025-02-03T01:30:32ZengWileyAdvances in High Energy Physics1687-73571687-73652017-01-01201710.1155/2017/78769427876942Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter GroupsÁngel Ballesteros0N. Rossano Bruno1Francisco J. Herranz2Departamento de Física, Universidad de Burgos, 09001 Burgos, SpainDepartamento de Física, Universidad de Burgos, 09001 Burgos, SpainDepartamento de Física, Universidad de Burgos, 09001 Burgos, SpainThe κ-deformation of the (2 + 1)D anti-de Sitter, Poincaré, and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter. The Drinfel’d-double and the Poisson–Lie structure underlying the κ-deformation are explicitly given, and the three quantum kinematical groups are obtained as quantizations of such Poisson–Lie algebras. As a consequence, the noncommutative (2 + 1)D spacetimes that generalize the κ-Minkowski space to the (anti-)de Sitter ones are obtained. Moreover, noncommutative 4D spaces of (time-like) geodesics can be defined, and they can be interpreted as a novel possibility to introduce noncommutative worldlines. Furthermore, quantum (anti-)de Sitter algebras are presented both in the known basis related to 2 + 1 quantum gravity and in a new one which generalizes the bicrossproduct one. In this framework, the quantum deformation parameter is related to the Planck length, and the existence of a kind of “duality” between the cosmological constant and the Planck scale is also envisaged.http://dx.doi.org/10.1155/2017/7876942 |
| spellingShingle | Ángel Ballesteros N. Rossano Bruno Francisco J. Herranz Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups Advances in High Energy Physics |
| title | Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups |
| title_full | Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups |
| title_fullStr | Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups |
| title_full_unstemmed | Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups |
| title_short | Noncommutative Relativistic Spacetimes and Worldlines from 2 + 1 Quantum (Anti-)de Sitter Groups |
| title_sort | noncommutative relativistic spacetimes and worldlines from 2 1 quantum anti de sitter groups |
| url | http://dx.doi.org/10.1155/2017/7876942 |
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