Recursive graphical solution of closed Schwinger–Dyson equations in φ4-theory. (I). Generation of connected and one-particle irreducible Feynman diagrams

Using functional derivatives with respect to the free correlation function we derive a closed set of Schwinger–Dyson equations in φ4-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.