RT info:eu-repo/semantics/article
T1 Noncommutative relativistic spacetimes and worldlines from 2 + 1 quantum (Anti-)de sitter groups
A1 Ballesteros Castañeda, Ángel
A1 Bruno, N. Rossano
A1 Herranz Zorrilla, Francisco José
K1 Physics
K1 Física
AB 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.
PB Hindawi Publishing Corporation
SN 1687-7357
YR 2017
FD 2017
LK http://hdl.handle.net/10259/4730
UL http://hdl.handle.net/10259/4730
LA eng
NO Ministerio deEconom´ıa y Competitividad (MINECO, Spain) under GrantsMTM2013-43820-P and MTM2016-79639-P (AEI/FEDER,UE), by Junta de Castilla y Le´on (Spain) under GrantsBU278U14 and VA057U16, and by the Action MP1405QSPACE from the European Cooperation in Science andTechnology (COST)
DS Repositorio Institucional de la Universidad de Burgos
RD 26-dic-2024