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 FJ, & 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].
Titolo: | Integrable geodesic motion on 3D curved spaces from non-standard quantum deformations RID F-2453-2010 | |
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Data di pubblicazione: | 2005 | |
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Citazione: | Ballesteros A, Herranz FJ, & 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]. | |
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. | |
Handle: | http://hdl.handle.net/11590/138011 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |