CONFORMAL SYMMETRY AND UNIVERSAL PROPERTIES OF QUANTUM HALL STATES

The low-lying excitations of a quantum Hall state on a disk geometry a re edge excitations. Their dynamics is governed by a conformal field t heory on the cylinder defined by the disk boundary and the time variab le. We give a simple and detailed derivation of this conformal field t heory for integer filling, starting from the microscopic dynamics of ( 2 + 1)-dimensional non-relativistic electrons in Landau levels. This c onstruction can be generalized to describe Laughlin's fractional Hall states via chiral bosonization, thereby making contact with the effect ive Chern-Simons theory approach. The conformal field theory dictates the finite-size effects in the energy spectrum. An experimental or num erical verification of these universal effects would provide a further confirmation of Laughlin's theory of incompressible quantum fluids.