Renormalization of non-Abelian gauge theories in a background-field gauge. II. Gauge-invariant operators

The Ward-Slavnov identities satisfied by the Green's functions with one insertion of a gauge-invariant operator are studied in the background-field gauge. As a consequence, the counterterms for a given gauge-invariant operator must satisfy a system of equations, whose general solution is found in the simplest cases of operators of low dimension (d6) or low twist (3) and conjectured in the general case. It then follows that the renormalized Green's functions satisfy the same Ward identities as the bare, regularized ones. We deduce a definite prescription for the practical calculation of the anomalous dimensions of gauge-invariant operators which do not vanish in the classical limit: this prescription is formulated in the background gauge or in the usual Fermi-type gauge.