Towards a Field Theory of Fractional Quantum Hall States

Abstract

We present a Chern-Simons theory of the fractional quantum Hall effect in which flux attachment is followed by a transformation that effectively attaches the correlation holes. We extract the correlated wave functions, compute the drift and cyclotron currents (due to inhomogeneous density), exhibit the Read operator and operators that create quasiparticles and quasiholes. We show how the bare kinetic energy can get quenched and replaced by one due to interactions. We find that for $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2$ the low energy theory has neutral quasiparticles and give the effective Hamiltonian and constraints.