On the derivation of quantum kinetic equations. I. Collision expansions

A straightforward scheme for deriving quantum kinetic equations is presented. It is based on Bogoliubov's initiai condition of vanishing correlations in the infinite past and consists in the elimination of an initial oneparticle Wigner function between two nonlinear functionals. By performing the elimination to second order in the density the quantum analog of the Choh-Uhlenbeck three-particle collision term is obtained. The scheme may be extended to include relativistic particles as well as particles with internal degrees of freedom.This investigation is part of the research program of the Stichting voor fundamenteel onderzoek der materie (FOM), which is financially supported by the Organisatie voor zuiver-wetenschappelijk onderzoek (ZWO).