## Abstract

Calogero-Moser systems are classical and quantum integrable multiparticle dynamics defined for any root system Delta. The quantum Calogero systems having 1/q(2) potential and a confining q(2) potential and the Sutherland systems with 1/sin(2) q potentials have 'integer' energy spectra characterized by the root system Delta. Various quantities of the corresponding classical systems, e.g. minimum energy, frequencies of small oscillations, the eigenvalues of the classical Lax pair matrices etc, at the equilibrium point of the potential are investigated analytically as well as numerically for all root systems. To our surprise, most of these classical data are also 'integers', or they appear to be 'quantized'. To be more precise, these quantities are polynomials of the coupling constant(s) with integer coefficients. The close relationship between quantum and classical integrability in Calogero-Moser systems deserves fuller analytical treatment, which would lead to better understanding of these systems and of integrable systems in general.

Original language | English |
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Pages (from-to) | 7017-7061 |

Number of pages | 45 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 35 |

Issue number | 33 |

DOIs | |

Publication status | Published - 23 Aug 2002 |

## Keywords

- ROOT SYSTEMS
- HYPERGEOMETRIC-FUNCTIONS
- BODY PROBLEMS
- LIE-ALGEBRAS
- LAX PAIRS
- MODELS
- CHAIN
- EXCHANGE
- SUPERSYMMETRY
- POTENTIALS