We propose a new procedure by using the recursive Green's functions which remove all the repetition terms from the time-independent perturbation series for finite-level quantum systems. These Green's functions are introduced as a generalization of the Brillouin-Wigner perturbation theory and the calculations of their diagonal elements can naturally give the effective propagators which are equal to the ones in the Feenberg perturbation theory.

arXiv:1904.00957Apr 1, 20190 citations

Why Self-Consistent Diagrammatic Perturbation Theory is `just' Perturbation Theory

Girish S. Setlur

In this short write-up we argue that self-consistent diagrammatic perturbation theory(i.e. Feynman diagrams) for the one-particle Green function is unable to capture some important qualitative features no matter how self-consistently the Green functions are obtained. This write-up is intended to highlight the short-comings of perturbation theory and also tout the advantages of the sea-boson technique(hep-th/9706006).

arXiv:cond-mat/9908269Aug 19, 19990 citations