Bi-Hamiltonian geometry and canonical spectral coordinates for the rational Calogero–Moser system

Abstract

We reconsider the rational Calogero–Moser system from the point of view of bi-Hamiltonian geometry. By using geometrical tools of the latter, we explicitly construct set(s) of spectral canonical coordinates, that is, complete sets of Darboux coordinates defined by the eigenvalues and the eigenvectors of the Lax matrix.