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Lattice dynamics of the Calogero-Sutherland-Moser (CSM) model

The purpose of this paper is to give a physical interpretation of all the Henon integrals of motion of the CSM model in the limit of small excitation energies. These integrals are first evaluated for the lattice at rest. It is then proved that the harmonic approximations of the Henon constants are integrals of motion of the harmonic CSM model and that they can be expressed as linear combinations of the action variables of the harmonic lattice. Moreover a method of calculation of the coefficients of these linear combinations is presented and illustrated.