Finite-Wavevector Electromagnetic Response of Fractional Quantized Hall States

A fractional quantized Hall state with filling fraction $\nu = p/(2mp+1)$ can be modeled as an integer quantized Hall state of transformed fermions, interacting with a Chern-Simons field. The electromagnetic response function for these states at arbitrary frequency and wavevector can be calculated using a semiclassical approximation or the Random Phase Approximation (RPA). However, such calculations do not properly take into account the large effective mass renormalization which is present in the Chern-Simons theory. We show how the mass renormalization can be incorporated in a calculation of the response function within a Landau Fermi liquid theory approach such that Kohn's theorem and the $f$-sum rules are properly satisfied. We present results of such calculations.