Projection-operator approach to a renormalized kinetic theory

Abstract

A renormalized kinetic theory is developed for the classical phase-space density correlation function by means of the projection-operator formalism. The technique consists of introducing a sequence of projection operators which project onto spaces involving successively larger numbers of particles. The first such operator is the Akcasu-Duderstadt projection operator, which yields a generalized Langevin equation (kinetic equation) for the correlation function. The structure of the memory function in this equation suggests a second projection operator, which is shown to lead to a two-body kinetic equation for one factor in the memory function. Further projection operators proceed similarly, and the result is a continued-fraction expansion of the correlation function. This expansion is renormalized in the sense that the interparticle potential always drops out in favor of static correlation functions. The expansion is shown to be equivalent to the result of the kinetic theory formulated by Gross. The analogous development for self-correlations is also given.