Noncommutative Chern-Simons Description of the Fractional Quantum Hall Edge

Noncommutative Chern-Simons (NCCS) theory is a workable description for the fractional quantum Hall fluid. We apply and generalize the NCCS theory to the physically important case with an edge. From relabeling symmetry of electrons and incompressibility of the fluid, we obtain a constraint and reduce the two-dimensional NCCS theory to a one-dimensional chiral Tomonaga-Luttinger liquid theory, which contains additional interaction terms. Further, we calculate one-loop corrections to the boson and electron propagators and obtain a new tunneling exponent, which agrees with experiments.