Renormalization Theory based on Flow Equations

TL;DR

This paper reviews rigorous renormalization theory using flow equations, focusing on Euclidean and Minkowski space analyses, with bounds on Schwinger functions and implications for quantum field theory.

Contribution

It provides a comprehensive overview of renormalization proofs based on flow equations, including new bounds and analyticity results for Schwinger functions in Euclidean and Minkowski spaces.

Findings

Established inductive bounds on regularized Schwinger functions

Presented sharpened bounds that are optimal for large momentum behavior

Discussed renormalizability and analyticity properties in Minkowski space

Abstract

I give an overview over some work on rigorous renormalization theory based on the differential flow equations of the Wilson-Wegner renormalization group. I first consider massive Euclidean $\phi_4^4$-theory. The renormalization proofs are achieved through inductive bounds on regularized Schwinger functions. I present relatively crude bounds which are easily proven, and sharpened versions (which seem to be optimal as regards large momentum behaviour). Then renormalizability statements in Minkowski space are presented together with analyticity properties of the Schwinger functions. Finally I give a short description of further results.