Generalized self-consistent field theory and the dielectric formulation of the many-body problem

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 is thus introduced into the energy so that for the particles interact only with a self-consistent field, for the particles interact dynamically among themselves with the correct field, and for intermediate values of 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 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.