COLLECTIVE-COORDINATE ACTION FOR CHARGED SIGMA-MODEL VORTICES IN FINITE GEOMETRIES

We apply the method of Lund to formulate a variational principle for the motion of charged vortices in an effective nonlinear Schrodinger field theory describing finite size two-dimensional quantum Hall samples under the influence of an arbitrary perpendicular magnetic field. Freezing out variations in the modulus of the effective field yields a U(1) sigma-model. A duality transformation on the sigma-model reduces the problem to finding the Green function for a related electrostatics problem. This duality connects the plasma analogy to the Laughlin wave function directly to a vortex gas description of the fractional quantum Hall effect.