Integrable potentials on spaces with curvature from quantum groups

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dc.creatorBallesteros, Angel
dc.creatorHerranz, Francisco J.
dc.creatorRagnisco, Orlando
dc.date2005-05-30
dc.date2005-08-08
dc.date.accessioned2026-07-07T10:46:36Z
dc.date.available2026-07-07T10:46:36Z
dc.descriptionA family of classical integrable systems defined on a deformation of the two-dimensional sphere, hyperbolic and (anti-)de Sitter spaces is constructed through Hamiltonians defined on the non-standard quantum deformation of a sl(2) Poisson coalgebra. All these spaces have a non-constant curvature that depends on the deformation parameter z. As particular cases, the analogues of the harmonic oscillator and Kepler--Coulomb potentials on such spaces are proposed. Another deformed Hamiltonian is also shown to provide superintegrable systems on the usual sphere, hyperbolic and (anti-)de Sitter spaces with a constant curvature that exactly coincides with z. According to each specific space, the resulting potential is interpreted as the superposition of a central harmonic oscillator with either two more oscillators or centrifugal barriers. The non-deformed limit z=0 of all these Hamiltonians can then be regarded as the zero-curvature limit (contraction) which leads to the corresponding (super)integrable systems on the flat Euclidean and Minkowskian spaces.
dc.description19 pages, 1 figure. Two references added
dc.identifierhttps://arxiv.org/abs/math-ph/0505081
dc.identifierhttp://arxiv.org/abs/math-ph/0505081
dc.identifierJ.Phys.A38:7129-7144,2005
dc.identifierdoi:10.1088/0305-4470/38/32/004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/183286
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.subjectExactly Solvable and Integrable Systems
dc.titleIntegrable potentials on spaces with curvature from quantum groups
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