Combinatorics of gauge fields

Abstract

Gauge field theories can be described by many different sets of Feynman rules, depending
\non the particular gauge chosen. In this paper a prescription for obtaining the
\nFeynman rules in different gauges is given. A rigorous combinatorial proof of the independence
\nof the S-matrix of the chosen gauge is presented. The proof is general and
\napplies to Yang-Mills type theories as well as to gravitation. For renormalizable Yang-
\nMills type theories it is shown that the renormalized theory is invariant with respect to
\nrenormalized gauge transformations.