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

We show that a Coulomb gas Vertex Operator representation of 2D Conformal Field Theory gives a complete description of Abelian Hall fluids: as a Euclidean theory in two space dimensions leads to the construction of the ground state wave functions for planar and toroidal geometry and characterizes the spectrum of low energy excitations; as a 1 + 1 Minkowski theory gives the corresponding dynamics of the edge states. The difference between a generic Hall fluid and states of the Jain's sequences is emphasized. In particular, the different structure of the lattice characterizing the indipendent Vertex Operators is exhibited; the 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 on the edges of a single charged mode and n - 1 neutral modes is discussed.