SPINNING BRAID-GROUP REPRESENTATION AND THE FRACTIONAL QUANTUM HALL-EFFECT

The path-integral approach to representing braid group is generalized for particles with spin. Introducing the notion of charged winding num ber in the super-plane, we represent the braid-group generators as hom otopically constrained Feynman kernels. In this framework, super Knizh nik-Zamolodchikov operators appear naturally in the hamiltonian, sugge sting the possibility of spinning nonabelian anyons. We then apply our formulation to the study of fractional quantum Hall effect (FQHE). A systematic discussion of the ground states and their quasi-hole excita tions is given. We obtain Laughlin, Halperin and Moore-Read states as exact ground-state solutions to the respective hamiltonians associated to the braid-group representations. The energy gap of the quasi-excit ation is also obtainable from this approach.