DISPERSION LAW OF EDGE WAVES IN THE QUANTUM HALL-EFFECT

We present a microscopic description of edge excitations in the quantu m Hall effect which is analogous to Feynman's theory of superfluids. A nalytic expressions for the excitation energies are derived in finite dots at integer filling. Our predictions are in excellent agreement wi th the results of a recent numerical diagonalization. In the limit of large N, where N is the number of electrons, the dispersion law is pro portional to q ln(1/q). For short range interactions it instead behave s as q3. The same results are also derived using hydrodynamic theory o f incompressible liquids.