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Título : Noncommutative relativistic spacetimes and worldlines from 2 + 1 quantum (Anti-)de sitter groups
Autor : Ballesteros, Ángel
Bruno, N. Rossano
Herranz Zorrilla, Francisco José
Publicado en: Advances in High Energy Physics. 2017, V. 2017, art. ID 7876942
Editorial : Hindawi Publishing Corporation
Fecha de publicación : 2017
ISSN : 1687-7357
DOI: 10.1155/2017/7876942
Resumen : 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.
Licencia: https://creativecommons.org/licenses/by/4.0/
URI : http://hdl.handle.net/10259/4730
Versión del editor: https://doi.org/10.1155/2017/7876942
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