Hedin's equations and enumeration of Feynman's diagrams

TL;DR

This paper solves Hedin's equations in zero dimension to systematically count Feynman diagrams for various quantities in a fermionic many-body theory, including within the GW approximation.

Contribution

It provides a novel perturbative solution to Hedin's equations in zero dimension for enumerating Feynman graphs, including GW approximation results.

Findings

Enumerates Feynman diagrams for self-energy, polarization, and vertex functions.

Provides counting numbers for diagrams in the GW approximation.

Offers a systematic combinatorial approach to diagram enumeration.

Abstract

Hedin's equations are solved perturbatively in zero dimension to count Feynman graphs for self-energy, polarization, propagator, effective potential and vertex function in a many-body theory of fermions with two-body interaction. Counting numbers are also obtained in the GW approximation.