FUNCTIONAL-DIFFERENTIAL EQUATION APPROACH TO MANY-PARTICLE SYSTEMS

A new many-body theoretical scheme based on the functional Schrodinger picture is presented. It is shown that the many-particle Schrodinger equation becomes a functional differential equation in this formalism. Using the Hubbard Hamiltonian and the BCS superconductivity as exampl es, the functional differential equations;the solved variationally to yield both the symmetry conserving and the symmetry breaking mean-fiel d solutions. Extension of the theory to finite temperature is also dis cussed using the density matrix formalism. This formalism is shown to lead to successful calculations of the Helmholtz free energy and the t otal energy of the electron gas system.