Effective vector-field theory and long-wavelength universality of the fractional quantum Hall effect

Abstract

We report on an effective vector-field theory of the fractional quantum Hall effect that takes into account projection to Landau levels. The effective theory refers to neither the composite-boson nor composite-fermion picture, but properly reproduces the results consistent with them, thus revealing the universality of the long-wavelength characteristics of the quantum Hall states. In particular, the dual-field Lagrangian of Lee and Zhang is obtained, and an argument is given to verify the identification by Goldhaber and Jain of a composite fermion as a dressed electron. The generalization to double-layer systems is also remarked.