SELFCONSISTENT APPROXIMATIONS IN MORIS THEORY

The constitutive quantities in Mori's theory, the residual forces, are expanded in terms of time-dependent correlation functions and product s of operators at t = 0, where it is assumed that the time derivatives of the observables are given by products of them. As a first conseque nce the Heisenberg dynamics of the observables are obtained as an expa nsion of the same type. The dynamic equations for correlation function s result to be selfconsistent nonlinear equations of the type known fr om mode-mode coupling approximations. The approach yields a necessary condition for the validity of the presented equations. As a third cons equence the static correlations can be calculated from fluctuation-dis sipation theorems, if the observables obey a Lie algebra. For a simple spin model the convergence of the expansion is studied. As a further test, dynamic and static correlations are calculated for a Heisenberg ferromagnet at low temperatures, where the results are compared to tho se of a Holstein-Primakoff treatment.