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

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

1993-07-13

arxiv.org/abs/hep-th/9307087v1

Phys.Lett. B315 (1993) 124-128

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, CCNY-HEP-93/2 plain tex

Scientific paper

10.1016/0370-2693(93)90168-H

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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