The maximal superintegrability of the intrinsic harmonic oscillator potential on N-dimensional spaces with constant curvature is revisited from the point of view of sl(2)-Poisson coalgebra symmetry. It is shown how this algebraic approach leads to a straightforward definition of a new large family of quasi-maximally superintegrable perturbations of the intrinsic oscillator on such spaces. Moreover, the generalization of this construction to those N-dimensional spaces with non-constant curvature that are endowed with sl(2)-coalgebra symmetry is presented. As the first examples of the latter class of systems, both the oscillator potential on an N-dimensional Darboux space as well as several families of its quasi-maximally superintegrable anharmonic perturbations are explicitly constructed.
Ballesteros, A., Enciso, A., Herranz, F.j., Ragnisco, O. (2008). Superintegrable Anharmonic Oscillators on N-dimensional Curved Spaces RID B-5702-2011 RID F-2453-2010. JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 15, 43-52 [10.2991/jnmp.2008.15.s3.5].
Superintegrable Anharmonic Oscillators on N-dimensional Curved Spaces RID B-5702-2011 RID F-2453-2010
RAGNISCO, Orlando
2008-01-01
Abstract
The maximal superintegrability of the intrinsic harmonic oscillator potential on N-dimensional spaces with constant curvature is revisited from the point of view of sl(2)-Poisson coalgebra symmetry. It is shown how this algebraic approach leads to a straightforward definition of a new large family of quasi-maximally superintegrable perturbations of the intrinsic oscillator on such spaces. Moreover, the generalization of this construction to those N-dimensional spaces with non-constant curvature that are endowed with sl(2)-coalgebra symmetry is presented. As the first examples of the latter class of systems, both the oscillator potential on an N-dimensional Darboux space as well as several families of its quasi-maximally superintegrable anharmonic perturbations are explicitly constructed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.