ABSTRACT

This chapter provides a nice application of the formalism of second quantization to the fractional quantum Hall effect. Throughout this chapter we will stay in the operator formalism and make no use of functional integrals. Whereas in the previous chapters we worked in the grand canonical ensemble, the fractional quantum Hall effect is usually discussed in the canonical ensemble which is mainly due to the huge degeneracy of the noninteracting system. For filling factors less than one, a suitable approximation is to consider only the contributions in the lowest Landau level. This projection of the many-body Hamiltonian onto the lowest Landau level can be done very easily with the help of annihilation and creation operators.