# Infinite symmetry in the quantum Hall effect

@article{Cappelli1993InfiniteSI, title={Infinite symmetry in the quantum Hall effect}, author={Andrea Cappelli and Carlo A. Trugenberger and Guillermo R. Zemba}, journal={Nuclear Physics}, year={1993}, volume={396}, pages={465-490} }

Abstract Free planar electrons in a uniform magnetic field are shown to possess the dynamical symmetry of area-preserving diffeomorphisms (W-infinity algebra). Intuitively, this is a consequence of gauge invariance, which forces dynamics to depend only on the flux. The infinity of generators of this symmetry act within each Landau level, which is infinite dimensional in the thermodynamic limit. The incompressible ground states corresponding to completely filled Landau levels (integer quantum…

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Abstract The Laughlin states for N interacting electrons at the plateaus of the fractional Hall effect are studied in the thermodynamic limit of large N . It is shown that this limit leads to the…

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In this lecture, I shall outline what I believe to be the correct fundamental picture of the fractional quantum Hall effect. The principal features of this picture are that the 1/3 state and its…