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arXiv · 0707.3769

Superintegrability on sl(2)-coalgebra spaces

Angel Ballesteros·Francisco J. Herranz·Orlando Ragnisco
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Abstract

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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Angel Ballesteros, Francisco J. Herranz, Orlando Ragnisco. 2007-07-25. Superintegrability on sl(2)-coalgebra spaces. https://doi.org/10.1134/s1063778808050074

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