Collective excitations in the Ginzburg-Landau theory of the fractional quantum Hall effect

The collective excitations of the fractional-quantum-Hall liquid are studied within the Ginzburg-Landau theory. We show that (1) Gaussian fluctuations of the phase of the order parameter correspond to the cyclotron mode with an energy gap of {}ωc at q=0 and a contribution to the static structure factor proportional to {}q² as q{→}0, in accordance with Kohn's theorem, and (2) vortex-antivortex fluctuations give rise to the lowest-Landau-level collective mode with an energy gap that depends only on the Coulomb energy and a static structure factor that vanishes as {}q⁴ as q{→}0.