  We consider the perturbative renormalization of the Schwinger-Dyson
functional, which is the generating functional of the expectation values of the
products of the composite operator given by the field derivative of the action.
It is argued that this functional plays an important role in the topological
Chern-Simons and BF quantum field theories. It is shown that, by means of the
renormalized perturbation theory, a canonical renormalization procedure for the
Schwinger-Dyson functional is obtained. The combinatoric structure of the
Feynman diagrams is illustrated in the case of scalar models. For the
Chern-Simons and the BF gauge theories, the relationship between the
renormalized Schwinger-Dyson functional and the generating functional of the
correlation functions of the gauge fields is produced.
