Schur functions, chiral bosons, and the quantum-Hall-effect edge states

Abstract

I demonstrate how the many-body wave function may be used to describe the bosonization of the edge excitations of a droplet of ν=1 quantum-Hall liquid. In particular, I exhibit an isomorphism between the charge-neutral edge-state excitations of the droplet and the space of universal symmetric polynomials. There are two natural bases for this space; the first, the Schur functions, correspond to the fermion picture; the second, generated by the power sums, yields the Bose picture and the Kac-Moody algebra. I also show explicitly how the loop group LU(1) acts to create the coherent-state deformations of the droplet shape used in path-integral bosonization and in the quantization of chiral bosons.