Classical Calogero Model and Matrix Model

Abstract

It is proved that the classical Calogero model is a realization of the U(1) current algebra. The relations with the hermitian one-matrix model are explicitly shown. In particular, the coupling constants in the potential of the matrix model are identified as the “time” variables of the classical Calogero model, which are conjugate to the conserved quantities. Furthermore, the Calogero model is related to the integrable nonlinear evolution equations.