Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature

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dc.creatorRagnisco, Orlando
dc.creatorBallesteros, Angel
dc.creatorHerranz, Francisco J.
dc.creatorMusso, Fabio
dc.date2006-11-16
dc.date2007-02-14
dc.date.accessioned2026-07-07T09:34:26Z
dc.date.available2026-07-07T09:34:26Z
dc.descriptionAn infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden non-standard quantum sl(2,R) Poisson coalgebra symmetry. As a concrete application, one of this Hamiltonians is shown to generate the geodesic motion on certain manifolds with a non-constant curvature that turns out to be a function of the deformation parameter z. Moreover, another Hamiltonian in this family is shown to generate geodesic motions on Riemannian and relativistic spaces all of whose sectional curvatures are constant and equal to the deformation parameter z. This approach can be generalized to arbitrary dimension by making use of coalgebra symmetry.
dc.descriptionThis is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/math-ph/0611040
dc.identifierhttp://arxiv.org/abs/math-ph/0611040
dc.identifierSIGMA 3 (2007), 026, 20 pages
dc.identifierdoi:10.3842/SIGMA.2007.026
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159492
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.subjectExactly Solvable and Integrable Systems
dc.subject37J35; 17B37
dc.titleQuantum Deformations and Superintegrable Motions on Spaces with Variable Curvature
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