Response Function of the Fractional Quantized Hall State on a Sphere I: Fermion Chern-Simons Theory

Abstract

Using a well known singular gauge transformation, certain fractional quantized Hall states can be modeled as integer quantized Hall states of transformed fermions interacting with a Chern-Simons field. In previous work we have calculated the electromagnetic response function of these states at arbitrary frequency and wavevector by using the Random Phase Approximation (RPA) in combination with a Landau Fermi Liquid approach. We now adopt these calculations to a spherical geometry in order to facilitate comparison with exact diagonalizations performed on finite size systems.