Green’s Functions and Perturbation Theory

D. I. Kadyrov

M. N. Aliev

M. N. Aliev, V. S. Tagiyev

Ishida, K.

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.

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).