MICROSCOPIC PICTURE OF A CHIRAL LUTTINGER LIQUID - COMPOSITE FERMION THEORY OF EDGE STATES

We derive a microscopic theory of the composite fermions describing th e low-lying edge excitations in the fractional quantum Hall liquid. Us ing the composite fermion transformation, one finds that the edge stat es of the v=1/m system in a disk sample are described by, in the one d imensional limit, the Calogero-Sutherland model with other interaction s between the composite fermions as perturbations. It is shown that a large class of short-range interactions renormalize only the Fermi vel ocity while the exponent g=v=1/m is invariant under the condition of c hirality. By taking the sharp edge potential into account, we obtain a microscopic justification of the chiral Luttinger liquid model of the fractional quantum Hall edge states. The approach applied to the v=1/ m system can be generalized to the other edge states with odd denomina tor filling factors.