Introduction to bosonization

Abstract

This is a pedagogical introduction to the general technique of bosonization of one-dimensional systems starting from scratch and assuming very little besides basic quantum mechanics and second quantization. The formalism is developed in a self-contained fashion and applied to the spinless and spin-1/2 Luttinger models, working out both single and two particle correlation functions. The implications of these results for the specific cases of the (anisotropic) Heisenberg and the Hubbard models are discussed. Although everything in these notes can be found in the published literature, detailed and explicit calculations of most of the results are given, which may prove useful to beginning graduate students or researchers in this area.