EFFECTIVE LAGRANGIAN, CASIMIR ENERGY AND CONFORMAL FIELD-THEORY DESCRIPTION OF THE QUANTUM HALL-EFFECT

By using the Girvin-MacDonald effective Lagrangian for the Hall fluid system at filling nu = 1 we are able to evaluate the ground-state ener gy for a cylinder of infinite length. That is done by using the topolo gical properties of the edge vacuum in the thermodynamic limit, N-e -- > infinity, nu = 1 fixed. From the vacuum energy we extract the value of the Casimir energy for both filling nu = 1 and nu = 1/m. The result s obtained fix the central charge c of the underlying 2D Conformal Fie ld Theory at c = 1. This correspondence is further analyzed by using t he bosonic realization of the Kac-Moody algebra on the edge vacuum. Th en the off-diagonal long-range order of the effective theory can be se en as an equivalent description of the topological order typical of th e 2D CFT.