Superintegrability on sl(2)-coalgebra spaces

Details Superintegrability on sl(2)-coalgebra spaces Superintegrability on sl(2)-coalgebra spaces

2007-07-25

arxiv.org/abs/0707.3769v1

Phys.Atom.Nucl.71:812-818,2008

Physics

Mathematical Physics

12 pages. Based on the contribution presented at the "XII International Conference on Symmetry Methods in Physics", Yerevan (A

Scientific paper

10.1134/S1063778808050074

We review a recently introduced set of N-dimensional quasi-maximally superintegrable Hamiltonian systems describing geodesic motions, that can be used to generate "dynamically" a large family of curved spaces. From an algebraic viewpoint, such spaces are obtained through kinetic energy Hamiltonians defined on either the sl(2) Poisson coalgebra or a quantum deformation of it. Certain potentials on these spaces and endowed with the same underlying coalgebra symmetry have been also introduced in such a way that the superintegrability properties of the full system are preserved. Several new N=2 examples of this construction are explicitly given, and specific Hamiltonians leading to spaces of non-constant curvature are emphasized.

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