Superintegrable potentials on 3D Riemannian and Lorentzian spaces with nonconstant curvature

Journal Article · Mon Feb 15 04:00:00 EST 2010 · Physics of Atomic Nuclei

DOI:https://doi.org/10.1134/S1063778810020092· OSTI ID:21443611

Ballesteros, A ^[1]; Enciso, A ^[2]; Ragnisco, O ^[3]

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1. Universidad de Burgos, Departamento de Fisica, Facultad de Ciencias (Spain)
2. Universidad Complutense, Departamento de Fisica Teorica II (Spain)
3. Universita di Roma Tre and Istituto Nazionale di Fisica Nucleare sezione di Roma Tre, Dipartimento di Fisica (Italy)

A quantum sl(2,R) coalgebra (with deformation parameter z) is shown to underly the construction of a large class of superintegrable potentials on 3D curved spaces, that include the nonconstant curvature analog of the spherical, hyperbolic, and (anti-)de Sitter spaces. The connection and curvature tensors for these 'deformed' spaces are fully studied by working on two different phase spaces. The former directly comes from a 3D symplectic realization of the deformed coalgebra, while the latter is obtained through a map leading to a spherical-type phase space. In this framework, the nondeformed limit z {yields} 0 is identified with the flat contraction leading to the Euclidean and Minkowskian spaces/potentials. The resulting Hamiltonians always admit, at least, three functionally independent constants of motion coming from the coalgebra structure. Furthermore, the intrinsic oscillator and Kepler potentials on such Riemannian and Lorentzian spaces of nonconstant curvature are identified, and several examples of them are explicitly presented.

• OSTI ID: 21443611
• Journal Information: Physics of Atomic Nuclei, Journal Name: Physics of Atomic Nuclei Journal Issue: 2 Vol. 73; ISSN 1063-7788; ISSN PANUEO
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANTI DE SITTER SPACE
CONFIGURATION
ELECTRONIC EQUIPMENT
EQUIPMENT
EUCLIDEAN SPACE
HAMILTONIANS
HYPERBOLIC CONFIGURATION
LIE GROUPS
LORENTZ GROUPS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MINKOWSKI SPACE
OSCILLATORS
PHASE SPACE
POINCARE GROUPS
POTENTIALS
QUANTUM OPERATORS
RIEMANN SPACE
SL GROUPS
SPACE
SPHERICAL CONFIGURATION
SYMMETRY GROUPS
THREE-DIMENSIONAL CALCULATIONS