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

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.