On the construction of renormalized gauge theories using renormalization group techniques

TL;DR

This paper presents a detailed construction of renormalized gauge theories using Wilson renormalization group techniques, focusing on symmetry preservation and short-distance behavior analysis.

Contribution

It introduces a self-contained method for constructing renormalized gauge theories via Wilson RG, including symmetry restoration at the quantum level.

Findings

Verification of Wilson short distance expansion.

Demonstration of symmetry breaking compensation with counter terms.

Analysis of $SU(2)$ gauge symmetry at quantum level.

Abstract

The aim of these lectures is to describe a construction, as self-contained as possible, of renormalized gauge theories. Following a suggestion of Polchinski, we base our analysis on the Wilson renormalization group method. After a discussion of the infinite cut-off limit, we study the short distance properties of the Green functions verifying the validity of Wilson short distance expansion. We also consider the problem of the extension to the quantum level of the classical symmetries of the theory. With this purpose we analyze in details the breakings induced by the cut-off in a $SU(2)$ gauge symmetry and we prove the possibility of compensating these breakings by a suitable choice of non-gauge invariant counter terms.