Renormalization of Composite Operators in Non-Abelian Gauge Theories

Abstract

Renormalization of composite operators (at zero momentum transfer) is discussed in non-Abelian gauge theories. Composite operators are inserted into Green's functions by differentiating Z, the generating functional for Green's functions, with respect to the parameters coupled to the composite operators. In the case of the field strength tensor with no coupling parameter, it is possible to have the form of [Formula: see text] by rescaling gauge fields as Aμa → Aμa/g. Then the renormalization of [Formula: see text] can be carried out by the differentiation [Formula: see text]. By doing this, the renormalization procedure is different from the previous work of Kluberg–Stern and Zuber. The procedure of this paper naturally leads to the proper basis of operators which makes the triangular renormalization matrix. Explicit forms for the relation between bare and renormalized composite operators are presented, with the dimensional regularization and minimal subtraction scheme.