The Green’s Function Method

Abstract

This chapter introduces the methods of quantum field theory as it appies to many-particle systems, particularly to superconductors. It focuses the ideas underlying the Green's function method, that is useful in the study of superconductivity. In dealing with an electron-phonon system it is reasonably realistic to approximate the effects of the phonons by an effective interaction between electrons that is of short range in space and retarded in time. It is especially appropriate to study the Green's function method in connection with the theory of superconductivity, because there are two reasons for this. The superconductor is the first system in solid-state physics in which the interaction between electrons qualitatively changes the spectrum of excitations. The other reason is the interaction that causes superconductivity is not describable by an ordinary potential: An electronic charge fluctuation with a frequency just below a characteristic frequency of the ionic lattice excites in the lattice a resonant sympathetic vibration that overcompensates for the electronic charge.