Renormalization group theory of effective field theory models in low dimensions

TL;DR

This lecture note explains the renormalization group approach to key low-dimensional field theory models like the sigma, phi^4, and sine-Gordon models using dimensional regularization to derive their beta functions.

Contribution

It provides a detailed explanation of the renormalization group method applied to universal low-dimensional models using dimensional regularization.

Findings

Derivation of beta functions for key models

Application of dimensional regularization in low dimensions

Analysis of universal field theoretic models

Abstract

This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We consider the models that are universal and frequently appear in physics, both in high-energy physics and condensed-matter physics. They are the non-linear sigma model, the $\phi^4$ model and the sine-Gordon model. We use the dimensional regularization method to regularize the divergence and derive the renormalization group equations called the beta functions. The dimensional method is described in detail.