Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-01-30
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, LaTeX
Scientific paper
The kappa-deformation of the 2+1 anti-de Sitter, Poincare and de Sitter groups is studied within a unified approach by considering explicitly the curvature of the spacetime (cosmological constant) as a parameter. The Drinfel'd-double construction as well as the Poisson-Lie structure underlying the kappa-deformation are explicitly given, and the three quantum groups are obtained as Weyl quantizations of such Poisson-Lie algebras. As a consequence, the non-commutative 2+1 spacetimes and 4D spaces of worldlines are derived. The former generalize the kappa-Minkowski space to the (anti)de Sitter ones, and the latter can be interpreted as a new possibility to introduce non-commutative velocity spaces. Furthermore, provided that the deformation parameter is identified with the Planck length, quantum (anti)de Sitter algebras are presented both in the known basis arising in 2+1 quantum gravity and in a new one which generalizes the bicrossproduct kappa-Poincare basis. Finally, the existence of a kind of "duality" between the cosmological constant and the Planck length is also commented.
Ballesteros Angel
Bruno Nicola Rossano
Herranz Francisco J.
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