Renormalization: an advanced overview

TL;DR

This paper provides an advanced overview of various renormalization techniques in quantum field theory, including multi-scale analysis, functional methods, and loop-vertex expansion, aiming to bridge gaps between different approaches.

Contribution

It synthesizes and compares multiple renormalization methods in QFT, offering insights beyond standard textbooks and connecting different specialized techniques.

Findings

Provides a comprehensive comparison of renormalization approaches

Highlights the connections between perturbative and non-perturbative methods

Aims to bridge gaps between different communities in QFT

Abstract

We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods \`a la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While each of these is quite well-established, they go beyond standard QFT textbook material, and may be little-known to specialists of each other approach. This review is aimed at bridging this gap.