Superintegrable Deformations of the Smorodinsky-Winternitz Hamiltonian
Mathematical Physics
2019-07-16 v1 math.MP
Quantum Algebra
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.math-ph/0412067,
title = {Superintegrable Deformations of the Smorodinsky-Winternitz Hamiltonian},
author = {Angel Ballesteros Francisco J. Herranz and Fabio Musso and Orlando Ragnisco},
journal= {arXiv preprint arXiv:math-ph/0412067},
year = {2019}
}
Comments
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