Generalized Pinch Technique and the Background Field Method in General Gauges

Abstract

It is shown that Cornwall's pinch technique can be extended in a consistent diagrammatic way, so as to describe general background field gauges in Yang-Mills theories. The resulting one-loop Green's functions are found to obey Ward identities identical to those derived from the classical action at the tree level. This generalization of the pinch technique may hence be related to the background field method implemented with novel gauge-fixing conditions invariant under background field gauge transformations. To one loop, the connection between the generalized pinch technique and the background field method in covariant and in non-covariant gauges is explicitly demonstrated.