Folded diagrams — a new tool for deriving exact nonlinear kinetic equations local in time

As in the effective interaction problem of nuclear physics, folding of diagrams is found to be a most effective way for deriving exact kinetic equations which are instantaneous or local in time. The diagrams obtained are explicitly depicting the microscopic events implicitly contained in the collision operator of the Green-Cohen cluster expansion method. Higher order distribution functions fs(t), s = 2, 3, …, are expressed in terms of f1(t) by means of folded diagrams, too. The relation between instantaneous and retarded kinetic equations are discussed. A new generalization of the Boltzmann equation for a strongly inhomogeneous system is obtained and the Choh-Uhlenbeck collision operator is rederived.