Combinatorics of gauge fields

Abstract

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