Half-filled Landau level as a Fermi liquid of dipolar quasiparticles

In this paper we study the relation between the conventional Fermion-Chern- Simons (FCS) theory of the half-filled Landau level (v = 1/2), and alternat e descriptions that are based on the notion of neutral quasiparticles that carry electric-dipole moments. We have previously argued that these two app roaches are equivalent, and that, e.g., the finite compressibility obtained in the FCS approach is also obtained from the alternate approach, provided that one properly takes into account a peculiar symmetry of the dipolar qu asiparticles-the invariance of their energy to a shift of their center of m ass momentum. Here, we demonstrate the equivalence of these two approaches in detail. We first study a model where the charge and flux of each fermion is smeared over a radius Q(-1) where results can be calculated to leading order in the small parameter Q/k(F). We study two dipolar-quasiparticle des criptions of the v = 1/2 state in the small-Q model and confirm that they y ield the same density-response function as in the FCS approach. We also stu dy the single-particle Green's function and the effective mass, for one for m of dipolar quasiparticles, and find the effective mass to be infrared div ergent, exactly as in the FCS approach. Finally, we propose a form for a Fe rmi-liquid theory for the dipolar quasiparticles, which should be valid in the physical case where Q is infinite. [S0163-1829(99)05119-X].