THEORY OF ARBITRARILY POLARIZED QUANTUM HALL STATES - FILLING FRACTIONS AND WAVE-FUNCTIONS

We propose a global model which accounts for almost all the observed q uantum Hall states in terms of an Abelian doubler of Chern-Simons gaug e fields, with the strength of the Chern-Simons term given by a coupli ng matrix. The model is employed within the composite fermion picture. We then determine the many body wave functions for arbitrarily polari zed quantum Hall states by employing the doublet model which describes arbitrarily polarized quantum Hall states. Our findings recover the w ell known fully polarized Laughlin wave functions and unpolarized Halp erin wave function for the filling fraction nu=2/5. We have also confi rmed by an explicit one-loop computation that the Hall conductivity do es indeed get quantized at those filling fractions that follow from th e model. Finally, we have given a physical picture for the non-analyti c nature of the wave functions, and shown that quantum fluctuations re store the Kohn mode.