Gauge theory approach towards an explicit solution of the (classical) elliptic Calogero-Moser system

• We discuss the relation of the trigonometric Calogero-Moser (CM) system to Yang-Mills gauge theories and its generalization to the elliptic case. This yields a linearization of the time evolution of the elliptic CM system and suggests two promising strategies for finding a fully explicit solution of this model. We also present a large class of integrable spin-particle systems generalizing the elliptic CM system.

Nyckelord

many-body problems

1 matrix model

integrable systems

cylinder

equations

bundles

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