An introduction to bosonization

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.