Abstract
We construct a W ∞ gauge field theory of electrons in the lowest Landau level. For this purpose we introduce an external gauge potential A such that its W ∞ gauge transformations cancel against the gauge transformation of the electron field. We then show that the electromagnetic interactions of electrons in the lowest Landau level are obtained through a non-linear realization of A in terms of the U (1) gauge potential A μ . As applications we derive the effective Lagrangians for circular droplets and for the ν = 1 quantum Hall system.
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