Integrable geodesic motion on 3D curved spaces from non-standard quantum deformations

Details Integrable geodesic motion on 3D curved spaces from non-standard quantum deformations Integrable geodesic motion on 3D curved spaces from non-standard quantum deformations

2005-08-19

arxiv.org/abs/math-ph/0508038v1

Czech. J. Phys. 55 (2005) 1327-1333

Physics

Mathematical Physics

7 pages. Communication presented at the 14th Int. Colloquium on Integrable Systems 14-16 June 2005, Prague, Czech Republic

Scientific paper

10.1007/s10582-006-0005-x

The link between 3D spaces with (in general, non-constant) curvature and quantum deformations is presented. It is shown how the non-standard deformation of a sl(2) Poisson coalgebra generates a family of integrable Hamiltonians that represent geodesic motions on 3D manifolds with a non-constant curvature that turns out to be a function of the deformation parameter z. A different Hamiltonian defined on the same deformed coalgebra is also shown to generate a maximally superintegrable geodesic motion on 3D Riemannian and (2+1)D relativistic spaces whose sectional curvatures are all constant and equal to z. This approach can be generalized to arbitrary dimension.

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