Lowest-Landau-level theory of the quantum Hall effect: The Fermi-liquid-like state of bosons at filling factor one

A theory for a Fermi-Liquid-like stare in a system of charged bosons at fil ling factor 1 is developed, working in the lowest Landau level. The approac h is based on a representation of the problem as fermions with a system of constraints, introduced by Pasquier and Haldane (unpublished). This makes t he system a gauge theory with gauge algebra W-infinity. The low-energy theo ry is analyzed based on a Hartree-Fock approximation and a corresponding co nserving approximation. This is shown to be equivalent to introducing a gau ge field, which at lung wavelengths gives an infinite-coupling U(1) gauge t heory, without a Chern-Simons term. The system is compressible, and the Fer mi-liquid properties are similar, but not identical, to those in the previo us U(1) Chern-Simons fermion theory. The fermions in the theory are effecti vely neutral, but carry a dipole moment. The density-density response, long itudinal conductivity, and current density are considered explicitly. [S016 3-1829(98)04748-1].