The link between 3D spaces with (in general non-constant) curvature and quantum deformations is presented. It is shown, how the non-standard deformation of a sl(2) Poisson coalgebra generates a family of integrable Hamiltonians, that represent geodesic motions on 3D manifolds with a non-constant curvature, that turns out to be a function of the deformation parameter z. A different Hamiltonian defined on the same deformed coalgebra is also shown to generate a maximally superintegrable geodesic motion on 3D Riemannian and (2+1)D relativistic spaces whose sectional curvatures are all constant and equal to z. This approach can be generalized to arbitrary dimension.

Ballesteros, A., Herranz, F.j., Ragnisco, O. (2005). Integrable geodesic motion on 3D curved spaces from non-standard quantum deformations RID F-2453-2010. CZECHOSLOVAK JOURNAL OF PHYSICS, 55(11), 1327-1333 [10.1007/s10582-006-0005-x].

Integrable geodesic motion on 3D curved spaces from non-standard quantum deformations RID F-2453-2010

RAGNISCO, Orlando
2005-01-01

Abstract

The link between 3D spaces with (in general non-constant) curvature and quantum deformations is presented. It is shown, how the non-standard deformation of a sl(2) Poisson coalgebra generates a family of integrable Hamiltonians, that represent geodesic motions on 3D manifolds with a non-constant curvature, that turns out to be a function of the deformation parameter z. A different Hamiltonian defined on the same deformed coalgebra is also shown to generate a maximally superintegrable geodesic motion on 3D Riemannian and (2+1)D relativistic spaces whose sectional curvatures are all constant and equal to z. This approach can be generalized to arbitrary dimension.
Ballesteros, A., Herranz, F.j., Ragnisco, O. (2005). Integrable geodesic motion on 3D curved spaces from non-standard quantum deformations RID F-2453-2010. CZECHOSLOVAK JOURNAL OF PHYSICS, 55(11), 1327-1333 [10.1007/s10582-006-0005-x].
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/11590/138011
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact