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

TL;DR

This paper critiques self-consistent diagrammatic perturbation theory for the one-particle Green function, highlighting its limitations and advocating for the sea-boson technique as a more effective alternative.

Contribution

It demonstrates the shortcomings of self-consistent diagrammatic perturbation theory and promotes the sea-boson method as a superior approach for capturing qualitative features.

Findings

Diagrammatic perturbation theory fails to capture certain qualitative features.

Sea-boson technique offers advantages over traditional perturbation methods.

Self-consistency does not resolve fundamental limitations of diagrammatic approaches.

Abstract

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).