Symmetry Aspects and Finite-Size Scaling of Quantum Hall Fluids

Abstract

The exactness and universality observed in the quantum Hall effect suggests the existence of a symmetry principle underlying Laughlin's theory. We review the role played by the infinite $W_{\infty }$ and conformal algebras as dynamical symmetries of incompressible quantum fluids and show how they predict universal finite-size effects in the excitation spectrum.Comment: 15 pages, CERN-TH-6784/93, LateX fil