Use of modified propagators in many-body perturbation theory

Abstract

In this paper we examine the efficacy of using modified propagators to sum arbitrary classes of diagrams to all orders in the many-body perturbation theory (MBPT) of Bruckner and Goldstone. The basic idea is to look upon any infinite series involving a skeleton insertion onto a subset of n internal lines as a modification or renormalisation of an n-body propagator. The Dyson equation then allows us to obtain this modified propagator involving a specific self-energy ∑ in terms of poles and residues. A subsequent grafting of this propagator onto the MBPT series for energy would then automatically incorporate the infinite series of appropriate skeleton insertions included in the modified propagator. The self-energy ∑ may be chosen to be either independent of or dependent on frequency, as dictated by convenience. Specific cases where the present viewpoint may serve as a viable alternative to other selective summation techniques are analysed.