Bosonization and effective vector-field theory of the fractional quantum Hall effect

Abstract

The electromagnetic characteristics of the fractional quantum Hall states are studied by formulating an effective vector-field theory that takes into account projection to the exact Landau levels from the beginning. The effective theory is constructed, via bosonization, from the electromagnetic response of an incompressible and uniform state. It does not refer to either the composite-boson or composite-fermion picture, but properly reproduces the results of the standard bosonic and fermionic Chern-Simons approaches, thus revealing the universality of the long-wavelength characteristics of the quantum Hall states and the associated quasiparticles. In particular, the dual-field Lagrangian of Lee and Zhang is obtained without invoking the composite-boson picture. An argument is also given to verify, within a vector-field version of the fermionic Chern-Simons theory, the identification by Goldhaber and Jain of a composite fermion as a dressed electron.