An introduction to bosonization

TL;DR

This paper provides an accessible introduction to bosonization, explaining its theoretical foundations, applications to the Tomonaga-Luttinger model, and extensions to non-Abelian cases within condensed matter physics.

Contribution

It offers a comprehensive overview of bosonization techniques, including heuristic explanations, exact solutions, and recent extensions, for the study of 1D strongly correlated electron systems.

Findings

Exact solution of the Tomonaga-Luttinger model

Introduction of non-Abelian bosonization

Clarification of fermion-boson quantum equivalence

Abstract

This is an expanded version of a lecture given at the {\it Workshop on Theoretical Methods for Strongly Correlated Fermions}, held at the {\it Centre de Recherches Math\'ematiques}, in Montr\'eal, from May 26 to May 30, 1999. After general comments on the relevance of field theory to condensed matter systems, the continuum description of interacting electrons in 1D is summarized. The bosonization procedure is then introduced heuristically, but the precise quantum equivalence between fermion and boson is also presented. Then the exact solution of the Tomonaga-Luttinger model is carried out. Two other applications of bosonization are then sketched. We end with a quick introduction to non-Abelian bosonization.