Fractional Quantum Hall Edge Electrons, Chiral Anomaly and the Berry Phase

It is shown that the deviation of fractional quantum Hall edge fluid from power law correlation functions with universal exponent $\alpha=1/\nu$ as observed in recent experiment may be explained when analyzed from the viewpoint of chiral anomaly and Berry phase. It is observed that at the edge anomaly vanishes and this induces a nonlocal effect in the construction of the electron creation operator in terms of the edge boson fields. This nonlocality is responsible for the deviation of the power law exponent from $\alpha=1/\nu$ of the edge fluid. There are gapless edge excitations described by chiral boson fields and the number of branches of chiral boson fields can be related to the polarization states of electrons in the bulk. We have noted that for fully polarized state at $\nu=\frac{1}{2m \pm 1}$ we will have a single branch whereas for partially polarized state at $\nu=\frac{n}{2mn \pm 1}$, with $n >1$ and odd, we will have $n$ branches. However for unpolarized state at $\nu=\frac{n}{2mn \pm 1}$ with $n$ even we will have two branches.