The cuboctahedric Higgs oscillator from the rational Calogero model
Abstract
We exclude the center of mass of the N-particle 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 four-particle system, these force centers define the vertexes of an Archimedean solid called a cuboctahedron.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- May 2009
- DOI:
- 10.1088/1751-8113/42/20/205206
- arXiv:
- arXiv:0808.0430
- Bibcode:
- 2009JPhA...42t5206H
- Keywords:
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- Mathematical Physics;
- Condensed Matter - Strongly Correlated Electrons;
- High Energy Physics - Theory
- E-Print:
- 8 pages, 2 figures, revised version accepted in J. Phys. A, new material on superintegrability and refs added