Curvature from quantum deformations

Details Curvature from quantum deformations Curvature from quantum deformations

2005-04-07

arxiv.org/abs/hep-th/0504065v1

Phys.Lett. B610 (2005) 107-114

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, LaTeX

Scientific paper

10.1016/j.physletb.2005.02.007

A Poisson coalgebra analogue of a (non-standard) quantum deformation of sl(2) is shown to generate an integrable geodesic dynamics on certain 2D spaces of non-constant curvature. Such a curvature depends on the quantum deformation parameter z and the flat case is recovered in the limit z\to 0. A superintegrable geodesic dynamics can also be defined in the same framework, and the corresponding spaces turn out to be either Riemannian or relativistic spacetimes (AdS and dS) with constant curvature equal to z. The underlying coalgebra symmetry of this approach ensures the existence of its generalization to arbitrary dimension.

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