Symbolic derivation of Dyson-Schwinger equations using Mathematica

The equations of motions of Green functions, the so-called Dyson-Schwinger equations, are a main tool for investigating the non-perturbative regimes of quantum field theories. The derivation becomes tedious as soon as one goes for higher vertex functions or when there are many different interactions. Using symbolic notation this can be done using simple algorithms leading to a considerable speed-up of the process. The method is suited to be cast into a symbolic programming language like Mathematica which also provides tools for producing the corresponding Feynman graphs. Given a Lagrangian and its symmetries the derivation of an arbitrary Dyson-Schwinger equation is possible. (author)