# Renormalization of SU(2) Yang-Mills theory with Flow Equations

## TL;DR

This paper proves the perturbative renormalizability of SU(2) Yang-Mills theory in four dimensions using Flow Equations, avoiding undefined mathematical objects and enabling physical renormalization conditions.

## Contribution

It provides a new proof of renormalizability based on Flow Equations that controls infrared singularities without relying on dimensionally regularized functionals.

## Key findings

- Establishes perturbative renormalizability of SU(2) Yang-Mills theory.
- Develops bounds on massless correlation functions.
- Demonstrates a renormalization approach using physical conditions.

## Abstract

We give a proof of perturbative renormalizability of SU(2) Yang--Mills theory in four-dimensional Euclidean space which is based on the Flow Equations of the renormalization group. The main motivation is to present a proof which does not make appear mathematically undefined objects (as for example dimensionally regularized generating functionals), which permits to parametrize the theory in terms of {\it physical} renormalization conditions, and which allows to control the singularities of the correlation functions of the theory in the infrared domain. Thus a large part of the proof is dedicated to bounds on massless correlation functions.