Linked-diagram theorem in many-body perturbation theory

Abstract

We revisit the so-called “linked-diagram theorem” of the effective interaction for many-body systems. We examine the theorem via the Rayleigh–Schrödinger perturbation theory in a coherent manner. First, we prove the theorem straightforwardly in closed and open systems at the same time. Second, we clarify that the “linked-diagram theorem” is still immature, and show how we can proceed on the basis of the present theory. The present work clarifies many aspects of the “linked-diagram theorem” that have not been elucidated so far.