Bosonization of a 2D electron gas in a magnetic field

Abstract

Starting from a Landau level description of a 2D fermion gas subject to a perpendicular uniform magnetic field, under the condition that there is a large integer number of filled Landau levels, we introduce a bosonization scheme for the low energy excitations of the system. We give an explicit construction of the fermion operator in terms of the bosons and show that the description of the elementary neutral excitations within a bosonic language provides a quadratic bosonic Hamiltonian for the interacting electron system which can be easily diagonalized.