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

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

1994-03-04

arxiv.org/abs/hep-th/9403025v2

Prog.Theor.Phys. 92 (1994) 293-308

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, UT-671

Scientific paper

10.1143/PTP.92.293

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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