Holomorphic Bundles and Many-Body Systems

Abstract

We show that spin generalization of elliptic Calogero-Moser system, elliptic extension of Gaudin model and their cousins can be treated as a degenerations of Hitchin systems. Applications to the constructions of integrals of motion, angle-action variables and quantum systems are discussed. Explicit formulas for the Lax operator on the higher genus surfaces are obtained in the Shottky parameterization. The constructions are motivated by the Conformal Field Theory, and their quantum counterpart can be treated as a degeneration of the critical level Knizhnik-Zamolodchikov-Bernard equations.

harvmac, 21 pages. In the revised version the formulas for the Lax operator on the arbitrary genus curve are added

References in corpus (2)

• Gaudin Model, Bethe Ansatz and Critical Level
• Relativistic Calogero-Moser model as gauged WZW theory

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