Calogero-moser models. I - A new formulation

A. J. Bordner, E. Corrigan, Ryu Sasaki

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60 Scopus citations


A new formulation of Calogero-Moser models based on root systems and their Weyl group is presented. The general construction of the Lax pairs applicable to all models based on the simply-laced algebras (ADE) are given for two types which we call 'root' and 'minimal'. The root type Lax pair is new; the matrices used in its construction bear a resemblance to the adjoint representation of the associated Lie algebra, and exist for all models, but they do not contain elements associated with the zero weights corresponding to the Cartan subalgebra. The root type provides a simple method of constructing sufficiently many number of conserved quantities for all models, including the one based on E8, whose integrability had been an unsolved problem for more than twenty years. The minimal types provide a unified description of all known examples of Calogero-Moser Lax pairs and add some more. In both cases, the root type and the minimal type, the formulation works for all of the four choices of potentials: the rational, trigonometric, hyperbolic and elliptic.

Original languageEnglish (US)
Pages (from-to)1107-1129
Number of pages23
JournalProgress of Theoretical Physics
Issue number6
StatePublished - Dec 1998

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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