Classical systems of infinitely many noninteracting particles

Abstract

It is proved that the C*‐algebra of observables of an infinite classical system is isomorphic to the group algebra on the test function space D. The physical dynamical system consisting of infinitely many noninteracting particles is studied. A particular class of states, called the quasifree states, is exhibited and their properties are studied. Some results on the spectral properties of monoparticle evolutions are obtained. Finally we give explicitly a solution of the classical KMS condition for these evolutions.