Abelian gauge invariance of non-Abelian gauge theories

Abstract

The ultraviolet asymptotic freedom of a large class of non-Abelian gauge theories enables the renormalization constants to be computed exactly in perturbation theory. This exact knowledge is used in investigating renormalized field equations of such theories. Many of them are shown to be invariant under an Abelian gauge transformation on the renormalized vector field. Consequences of the Abelian invariance are derived in the form of Ward-Takahashi identities for the renormalized proper vertices ${\Gamma }_R^{\cdots \mu \cdots }(\dots ,q,\dots ):q_{\mu }{\Gamma }_R^{\cdots \mu \cdots }(\dots ,q = 0,\dots ) = 0$.