2024-03-28T21:58:57Zhttps://riubu.ubu.es/oai/requestoai:riubu.ubu.es:10259/47302022-12-20T11:45:35Zcom_10259.4_2557com_10259_5086com_10259_2604col_10259.4_2558
2018-02-06T08:15:38Z
urn:hdl:10259/4730
Noncommutative relativistic spacetimes and worldlines from 2 + 1 quantum (Anti-)de sitter groups
Ballesteros Castañeda, Ángel
Bruno, N. Rossano
Herranz Zorrilla, Francisco José
The -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 -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 -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.
2018-02-06T08:15:38Z
2018-02-06T08:15:38Z
2017
info:eu-repo/semantics/article
1687-7357
http://hdl.handle.net/10259/4730
10.1155/2017/7876942
eng
Advances in High Energy Physics. 2017, V. 2017, art. ID 7876942
https://doi.org/10.1155/2017/7876942
info:eu-repo/grantAgreement/MINECO/MTM2013-43820-P
info:eu-repo/grantAgreement/MINECO/MTM2016-79639-P
info:eu-repo/grantAgreement/JCyL/BU278U14
info:eu-repo/grantAgreement/JCyL/VA057U16
info:eu-repo/grantAgreement/UE/COST-MP1405
http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
Attribution 4.0 International
Hindawi Publishing Corporation