The Fermion Chern-Simons Gauge Theory of Fractional Quantum Hall Effect for Electromagnetic Polarization Tensor

Unlike an earlier theory, by avoiding both the electromagnetic gauge field shift and the assumption of the zero average of electromagnetic field fluctuation the fermion Chern-Simons gauge theory is reformulated to obtain mean field solutions and a self-consistent expression of the electromagnetic polarization tensor in terms of the composite fermion picture for the systems of fractional quantum Hall effect. Thus the newly derived electromagnetic polarization tensor is shown to depend on the residual (effective) magnetic field `seen' by composite fermions rather than the statistical field, which differs from the earlier theory. The present theory reproduces the Hall conductance of fractional quantum Hall effect. The self-consistent picture of the composite fermion is maintained in all of our derivations: both the mean field solutions and the electromagnetic polarization tensor are described by the residual magnetic field seen by the composite fermions.