The diagrammatic method is one of the most powerful tools of theoretical physics. It allows us to efficiently organize perturbative computations in statistical physics, quantum many-body theory and quantum field theory. The main feature of this method is a representation of individual terms of a perturbative expansion as diagrams (graphs). Diagrams consist of vertices representing terms in the perturbation, lines representing pairings between vertices and, possibly, external legs.
There exist several kinds of diagrams. We will try to present them in a systematic way.
In Sect. 20.1 we present a diagrammatic formalism whose goal is to organize integration of polynomials with respect to a Gaussian measure. This formalism is used ...