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arXiv · hep-th/9307087

W_{\infty} Gauge Transformations and the Electromagnetic Interactions of Electrons in the Lowest Landau Level

B. Sakita
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Abstract

We construct a $W_{\infty}$ gauge field theory of electrons in the lowest Landau level. For this purpose we introduce an external gauge potential $\cal A $ such that its $W_{\infty}$ 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 $\cal A$ in terms of the $U(1)$ gauge potential $A^{\m}$. As applications we derive the effective Lagrangians for circular droplets and for the $\n =1$ quantum Hall system.

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B. Sakita. 1993-07-13. W_{\infty} Gauge Transformations and the Electromagnetic Interactions of Electrons in the Lowest Landau Level. https://doi.org/10.1016/0370-2693(93)90168-h

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