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The quantum angular Calogero-Moser model

  • Mikhail Feigin
  • Olaf LechtenfeldEmail author
  • Alexios P. Polychronakos
Article

Abstract

The rational Calogero-Moser model of n one-dimensional quantum particles with inverse-square pairwise interactions (in a confining harmonic potential) is reduced along the radial coordinate of \( {{\mathbb{R}}^n} \) to the ‘angular Calogero-Moser model’ on the sphere S n−1.We discuss the energy spectrum of this quantum system, its degeneracies and the eigenstates. The spectral flow with the coupling parameter yields isospectrality for integer increments. Decoupling the center of mass before effecting the spherical reduction produces a ‘relative angular Calogero-Moser model’, which is analyzed in parallel. We generalize our considerations to the Calogero-Moser models associated with Coxeter groups. Finally, we attach spin degrees of freedom to our particles and extend the results to the spin-Calogero system.

Keywords

Integrable Equations in Physics Integrable Field Theories 

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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • Mikhail Feigin
    • 1
  • Olaf Lechtenfeld
    • 2
    Email author
  • Alexios P. Polychronakos
    • 3
    • 4
  1. 1.School of Mathematics and StatisticsUniversity of GlasgowGlasgowU.K.
  2. 2.Institut für Theoretische Physik and Riemann Center for Geometry and PhysicsLeibniz Universität HannoverHannoverGermany
  3. 3.CCPP, Department of PhysicsNYUNew YorkU.S.A.
  4. 4.Physics DepartmentThe City College of the CUNYNew YorkU.S.A.

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