Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson

Abstract

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, $W_{\infty }$, 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.

16 pages

References in corpus (2)

• Bosonization of Nonrelativistic Fermions and W-infinity Algebra
• $W$-Infinity Ward Identities and Correlation Functions in the $C=1$ Matrix Model

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