Abstract
By performing the Gupta–Bleuler quantization of a chiral boson, we obtain the chiral constraints, which correspond to the lowest Landau level conditions. From these, the chiral vacuum is defined as the vacuum of admixtures of many-harmonic oscillators. We construct the wave function for edge states of a droplet of incompressible quantum Hall fluid, by solving Schrödinger's equation on the basis of the chiral vacuum. This bosonic function can describe the collective edge modes, which are fundamentally a many-body effect of fermions at the lowest Landau level. In detail, the neutral edge state of FQHE is described by the α = 1 chiral boson theory. The charged edge states are described by the α ≠ 1 chiral boson theory.
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