Rigidity, Functional Equations and the Calogero-Moser Model

Details Rigidity, Functional Equations and the Calogero-Moser Model Rigidity, Functional Equations and the Calogero-Moser Model

2000-05-22

arxiv.org/abs/nlin/0005046v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

10.1088/0305-4470/34/11/312

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 $V={1/6}\sum\limits_{i\neq
j}\wp(q_{i}-q_{j}) +const$.

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