A 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.

Ballesteros, A., Herranz, F.j., Ragnisco, O. (2005). Integrable potentials on spaces with curvature from quantum groups RID F-2453-2010. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 38(32), 7129-7144 [10.1088/0305-4470/38/32/004].

Integrable potentials on spaces with curvature from quantum groups RID F-2453-2010

RAGNISCO, Orlando
2005-01-01

Abstract

A 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.
2005
Ballesteros, A., Herranz, F.j., Ragnisco, O. (2005). Integrable potentials on spaces with curvature from quantum groups RID F-2453-2010. JOURNAL OF PHYSICS. A, MATHEMATICAL AND GENERAL, 38(32), 7129-7144 [10.1088/0305-4470/38/32/004].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/117843
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