An Introduction to Bosonization and Some of its Applications
This chapter discusses the technique of bosonization for studying systems of interacting fermions in one dimension. It reviews the low-energy properties of Fermi and Luttinger liquids and presents some of the relations between bosonic and fermionic operators in one dimension. The chapter explores these relations to calculate the correlation functions and the renormalization group properties of various operators for a system of spinless fermions. It explains the methods of bosonization to study the Heisenberg antiferromagnetic spin 1/2 chain, the Hubbard model in one dimension and transport in clean quantum wires and in the presence of isolated impurities. The basic idea of bosonization is that there are certain objects which can be calculated either in a fermionic theory or in a bosonic theory, and the two calculations give the same answer. The chapter also discusses another application of bosonization, which is to study transport, in particular the DC conductivity in one-dimensional wires of interacting fermions.