Superintegrable Deformations of the Smorodinsky-Winternitz Hamiltonian

Abstract

A constructive procedure to obtain superintegrable deformations of the classical Smorodinsky-Winternitz Hamiltonian by using quantum deformations of its underlying Poisson sl(2) coalgebra symmetry is introduced. Through this example, the general connection between coalgebra symmetry and quasi-maximal superintegrability is analysed. The notion of comodule algebra symmetry is also shown to be applicable in order to construct new integrable deformations of certain Smorodinsky-Winternitz systems.

17 pages. Published in "Superintegrability in Classical and Quantum Systems", edited by P.Tempesta, P.Winternitz, J.Harnad, W.Miller Jr., G.Pogosyan and M.A.Rodriguez, CRM Proceedings & Lecture Notes, vol.37, American Mathematical Society, 2004

References in corpus (1)

• Comodule algebras and integrable systems

Cited by in corpus (4)

• Superintegrability on Three-Dimensional Riemannian and Relativistic Spaces of Constant Curvature
• Maximally superintegrable Smorodinsky-Winternitz systems on the N-dimensional sphere and hyperbolic spaces
• Binary trees, coproducts, and integrable systems
• Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature