Holomorphic Bundles and Many-Body Systems
High Energy Physics - Theory
2009-10-28 v4 alg-geom
Algebraic Geometry
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.
Cite
@article{arxiv.hep-th/9503157,
title = {Holomorphic Bundles and Many-Body Systems},
author = {Nikita Nekrasov},
journal= {arXiv preprint arXiv:hep-th/9503157},
year = {2009}
}
Comments
harvmac, 21 pages. In the revised version the formulas for the Lax operator on the arbitrary genus curve are added