Generalized Self-Consistent Field Theory and the Dielectric Formulation of the Many-Body Problem

Abstract

A generalized self-consistent field (SCF) theory of many-particle systems is developed by modifying the usual functional relationship between energy and wave function. A parameter $\xi$, $0\le \xi \le 1$, is thus introduced into the energy so that for $\xi =0\mathrm{}$, the particles interact only with a self-consistent field, for $\xi =1\mathrm{}$ the particles interact dynamically among themselves with the correct field, and for intermediate values of $\xi$ both SCF and dynamical interactions occur. A systematic development of the theory is given for time-independent and time-dependent probelms, for finite temperatures, and for both uniform and nonuniform systems. The derivative with respect to $\xi$ of the total energy, of free energy, is expressed in terms of the dielectric function and an improved version of the dielectric formulation of the many-body problem thereby obtained. A brief discussion of the advantages of the method, possible applications, and further generalizations or extensions is included.