The Calogero-Moser Model Based On Doubly-Laced Lie Algebras

Abstract

The Calogero-Moser model is an one-dimensional dynamical system that describes N pairwise interacting particles on a line with nonlinear interaction potentials. These potentials are associated with the root system of the Simple Lie Algebras. The Calogero-Moser model is integrable, and its integrability is describe through the Lax pair operators built in the root system of the associated Lie algebra. In the present work, a new Lax pair operator for the Calogero-Moser model based on the Doubly Simply-Laced Lie algebras is presented. It is shown that the canonical equation of motion obtained from the Lax pair formulation and from the Hamiltonian formulation are consistent.