Multicenter Higgs oscillators and Calogero model
We show that the spherical part of N-particle Calogero model describes, after exclusion of the center of mass, the motion of the particle on (N − 2)-dimensional sphere interacting with N(N − 1)/2 force centers with Higgs oscillator potential. In the case of four-particle system these force centers are located at the vertexes of cuboctahedron. The geometry of the five-particle case is also investigated.
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- 4.D. Bonatsos, C. Daskaloyannis, and K. Kokkotas, Phys. Rev. A 50, 3700 (1994); E. G. Kalnins, W. Miller, Jr., and G. S. Pogosyan, J. Math. Phys. 41, 2629 (2000); A. Nersessian and G. Pogosyan, Phys. Rev. A 63, 020103 (2001); A. Ballesteros, F. J. Herranz, and O. Ragnisco, J. Phys. A 38, 7129 (2005); A. Ballesteros and F. J. Herranz, J. Phys. (N.Y.) A 40, F51 (2007); J. F. Carinena, M. F. Ranada, and M. Santander, Ann. Phys. 322, 2249 (2007).CrossRefMathSciNetADSGoogle Scholar
- 6.A. M. Perelomov, Integrable Systems of Classical Mechanics and Lie Algebras (Nauka, Moscow, 1989) [in Russian].Google Scholar