Rigidity, Functional Equations and the Calogero-Moser Model

Abstract

Suppose we have a natural Hamiltonian $H$ of $n$ particles on the line, centre of mass momentum $P$ and a further independent quantity $Q$, cubic in the momenta. If these are each $S_n$ invariant and mutually Poisson commute we have the Calogero-Moser system with potential $V=1/6\sum _{i\ne j}\wp (q_i-q_j)+const$.

8 pages, Latex. Talk presented at the Workshop on ``Mathematical Methods of Regular Dynamics" dedicated to the 150-th anniversary of Sophie Kovalevski

References in corpus (1)

• On Double-Elliptic Integrable Systems. 1. A Duality Argument for the case of SU(2)

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