ABELIAN HALL FLUIDS AND EDGE STATES - A CONFORMAL FIELD-THEORY APPROACH

We show that a Coulomb gas Vertex Operator representation of 2D Confor mal Field Theory gives a complete description of Abelian Hall fluids: as a Euclidean theory in two space dimensions leads to the constructio n of the ground state wave functions for planar and toroidal geometry and characterizes the spectrum of low energy excitations; as a 1 + 1 M inkowski theory gives the corresponding dynamics of the edge states. T he difference between a generic Hall fluid and states of the Jain's se quences is emphasized. In particular, the different structure of the l attice characterizing the indipendent Vertex Operators is exhibited; t he presence, in Jain's case, of of an ($) over cap U(1) X ($) over cap S ($) over cap U(n) extended algebra and the consequent propagation o n the edges of a single charged mode and n - 1 neutral modes is discus sed.