The cuboctahedric Higgs oscillator from the rational Calogero model
Abstract
We exclude the center of mass of the Nparticle rational Calogero model and consider the angular part of the resulting Hamiltonian. We show that it describes the motion of the particle on an (N  2)dimensional sphere interacting with N(N  1)/2 force centers with Higgs oscillator potential. In the case of a fourparticle system, these force centers define the vertexes of an Archimedean solid called a cuboctahedron.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 May 2009
 DOI:
 10.1088/17518113/42/20/205206
 arXiv:
 arXiv:0808.0430
 Bibcode:
 2009JPhA...42t5206H
 Keywords:

 Mathematical Physics;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 8 pages, 2 figures, revised version accepted in J. Phys. A, new material on superintegrability and refs added