An 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.

Ragnisco, O., Ballesteros, A., Herranz, F.j., Musso, F. (2007). Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature RID F-2453-2010 RID A-7283-2010. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 3.

Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature RID F-2453-2010 RID A-7283-2010

RAGNISCO, Orlando;
2007-01-01

Abstract

An 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.
2007
Ragnisco, O., Ballesteros, A., Herranz, F.j., Musso, F. (2007). Quantum Deformations and Superintegrable Motions on Spaces with Variable Curvature RID F-2453-2010 RID A-7283-2010. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 3.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/138010
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 12
social impact