Schwinger-Dyson Renormalization Group

TL;DR

This paper derives renormalization flow equations from Schwinger-Dyson equations, showing how Katanin's scheme emerges as a truncation, and explores higher-order functional relationships involving self-energy and vertices.

Contribution

It introduces a systematic derivation of renormalization group equations from Schwinger-Dyson equations up to third order and identifies a functional whose saddle point solves these equations.

Findings

Katanin's scheme is a simple truncation of Schwinger-Dyson derived equations.

Full renormalization group equations are provided up to third order.

A functional at fifth order relates self-energy and vertices with saddle point solutions.

Abstract

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.