Renormalized Schwinger–Dyson functional

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.