In this paper we study the relation between the conventional Fermion-Chern-Simons (FCS) theory of the half-filled Landau level (nu=1/2), and alternate descriptions that are based on the notion of neutral quasi-particles that carry electric dipole moments. We have previously argued that these two approaches 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 quasiparticles --- the invariance of their energy to a shift of their center of mass 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 descriptions of the nu=1/2 state in the small-Q model and confirm that they yield the same density response function as in the FCS approach. We also study the single-particle Greens function and the effective mass, for one form of dipolar quasiparticles, and find the effective mass to be infra-red divergent, exactly as in the FCS approach. Finally, we propose a form for a Fermi-liquid theory for the dipolar quasiparticles, which should be valid in the physical case where Q is infinite.
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