Linked Cluster Theorem and the Green's Function Equations of Motion for a Many Fermion System

摘要

The equations of motion for the general many-time causal Green's functions for a fermion system are iterated and shown not to lead to unlinked graphs, which is a general proof of the linked cluster theorem. An explicit expression is obtained for the perturbation expansion of an arbitrary Green's functions which is applied to the one and two particle Green's functions. By connecting lines systematically in a set of diagrams obtained from the equations of motion, the usual topologically different linked graphs and rules are generated. (Author)