We write a Ginzburg–Landau Hamiltonian for a charged order parameter interacting with a background electromagnetic field in 2 + 1 dimensions, which we propose as an effective theory for the fractional quantum Hall effect. We further propose to identify vortex excitations of the theory with Laughlin's fractionally charged quasiparticles. Using the method of Lund we derive a collective coordinate action for vortex defects in the order parameter and demonstrate that the vortices are charged. We examine the classical dynamics of the vortices and then quantize their motion, demonstrating that their peculiar classical motion is a result of the fact that the quantum motion takes place in the lowest Landau level. The classical and quantum motion in two-dimensional regions with boundaries is also investigated. The quantum theory is not invariant under magnetic translations. Magnetic translations add total time derivative terms to the collective action, but no extra constants of the motion result.
Bulk and edge properties of the Chern-Simons Ginzburg-Landau theory for the fractional quantum Hall effect
