Recursive Graphical Solution of Closed Schwinger-Dyson Equations in phi^4-Theory -- Part1: Generation of Connected and One-Particle Irreducible Feynman Diagrams

TL;DR

This paper develops a recursive graphical method to systematically generate all connected and one-particle irreducible Feynman diagrams in phi^4-theory using Schwinger-Dyson equations.

Contribution

It introduces a novel recursive graphical approach to derive and generate Feynman diagrams directly from Schwinger-Dyson equations in phi^4-theory.

Findings

Systematic generation of all relevant Feynman diagrams achieved.

Weights of diagrams computed explicitly.

Method simplifies diagrammatic calculations in quantum field theory.

Abstract

Using functional derivatives with respect to the free correlation function we derive a closed set of Schwinger-Dyson equations in phi^4-theory. Its conversion to graphical recursion relations allows us to systematically generate all connected and one-particle irreducible Feynman diagrams for the two- and four-point function together with their weights.