Schwinger-Dyson renormalization group

We use the Schwinger-Dyson equations as a starting point to derive renormalization flow equations. We show that Katanin's scheme arises as a simple truncation of these equations. We then give the full renormalization group equations up to third order in the irreducible vertex. Furthermore, we show that to the fifth order, there exists a functional of the self-energy and the irreducible four-point vertex whose saddle point is the solution of Schwinger-Dyson equations.

Figure 1

The diagrammatic representations of the SD equation (10) is given in (a), (b) represents Eq. (11), and (c) corresponds to Eq. (20).

Figure 2

The diagrammatic representations of the functional $\mathcal{F}$ defined in Eq. (33).