Maximal superintegrability on N-dimensional curved spaces
摘要
A unified algebraic construction of the classical Smorodinsky-Winternitz systems on the ND sphere, Euclidean and hyperbolic spaces through the Lie groups SO(N+1), ISO(N), and SO(N,1) is presented. Firstly, general expressions for the Hamiltonian and its integrals of motion are given in a linear ambient space , and secondly they are expressed in terms of two geodesic coordinate systems on the ND spaces themselves, with an explicit dependence on the curvature as a parameter. On the sphere, the potential is interpreted as a superposition of N+1 oscillators. Furthermore each Lie algebra generator provides an integral of motion and a set of 2N-1 functionally independent ones are explicitly given. In this way the maximal superintegrability of the ND Euclidean Smorodinsky-Winternitz system is shown for any value of the curvature.
引用
@article{arxiv.math-ph/0211012,
title = {Maximal superintegrability on N-dimensional curved spaces},
author = {A. Ballesteros and F. J. Herranz and M. Santander and T. Sanz-Gil},
journal= {arXiv preprint arXiv:math-ph/0211012},
year = {2009}
}
备注
8 pages, LaTeX