COLLECTIVE FIELD-THEORY OF THE FRACTIONAL QUANTUM HALL EDGE STATE ANDTHE CALOGERO-SUTHERLAND MODEL

Using the hydrodynamic collective field approximation for the v = 1/m fractional quantum Hall droplet dynamics we find that the low-energy e xcitations are described by c = 1 conformal field theory of a compact boson of radius root m. Using the conformal field theory method we sho w that the one-particle density matrix of the edge state interpolates between the chiral Luttinger liquid behavior [psi(dagger)(r)psi(0)] si milar to r(-m) and the Calogero-Sutherland model behavior [psi(dagger) (r)psi(0)] similar to r(-(m+1/m)/2) as the droplet width is varied con tinuously. The result suggests complementary relation between the two- dimensional quantum Hall droplet and the one-dimensional Calogero-Suth erland model.