FERMIONS IN THE LOWEST LANDAU-LEVEL - BOSONIZATION, W-INFINITY ALGEBRA, DROPLETS, CHIRAL BOSONS

We present field theoretical descriptions of massless (2 + 1) dimensional nonrelativistic fermions in an external magnetic field, in terms of a fermionic and bosonic second quantized language. An infinite dimensional algebra, W(infinity), appears as the algebra of unitary transformations which preserve the lowest Landau level condition and the particle number. In the droplet approximation it reduces to the algebra of area-preserving diffeomorphisms, which is responsible for the existence of a universal chiral boson lagrangian independent of the electrostatic potential. We argue that the bosonic droplet approximation is the strong magnetic field limit of the fermionic theory. The relation to the c = 1 string model is discussed.