How to relate the oscillator and Coulomb systems on spheres and pseudospheres?
Abstract
We show that the oscillators on a sphere and pseudosphere are related, by the so-called Bohlin transformation, with the Coulomb systems on the pseudosphere: the even states of an oscillator yields the conventional Coulomb system on pseudosphere, while the odd states yield the Coulomb system on pseudosphere in the presence of magnetic flux tube generating half spin. In the higher dimensions the oscillator and Coulomb(-like) systems are connected in the similar way. In particular, applying the Kustaanheimo-Stiefel transformation to the oscillators on sphere and pseudosphere, we obtained the preudospherical generalization of MIC-Kepler problem describing three-dimensional charge-dyon system.
Keywords
Cite
@article{arxiv.math-ph/0010049,
title = {How to relate the oscillator and Coulomb systems on spheres and pseudospheres?},
author = {Armen Nersessian},
journal= {arXiv preprint arXiv:math-ph/0010049},
year = {2011}
}
Comments
12 pages, Based on talk given at XXIII Colloquium on Group Theoretical Methods in Physics (July 31-August 5, 2000, Dubna)