$W_{\infty}$ algebra in the integer quantum Hall effects

Hiroo Azuma

doi:10.1143/ptp/92.2.293

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$W_{\infty}$ algebra in the integer quantum Hall effects

Hiroo Azuma

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Abstract

We investigate the $W_{\infty}$ algebra in the integer quantum Hall effects. Defining the simplest vacuum, the Dirac sea, we evaluate the central extension for this algebra. A new algebra which contains the central extension is called the $W_{1+\infty}$ algebra. We show that this $W_{1+\infty}$ algebra is an origin of the Kac-Moody algebra which determines the behavior of edge states of the system. We discuss the relation between the $W_{1+\infty}$ algebra and the incompressibility of the integer quantum Hall system.

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Hiroo Azuma. 1994-03-14. $W_{\infty}$ algebra in the integer quantum Hall effects. https://doi.org/10.1143/ptp%2F92.2.293

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