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VOLUME 82 | ISSUE 3 | PAGE 166
Non-Fermi liquid theory of the quantum Hall effects
A. M. Pruisken+, M. A. Baranov^{*\triangle}, I. S. Burmistrov^{+\square}
+ Institute for Theoretical Physics, University of Amsterdam, 1018 XE Amsterdam, The Netherlands
*Van der Waals-Zeeman Institute for Experimental Physics, University of Amsterdam, 1018 XE Amsterdam, The Netherlands
^\triangle RRC «Kurchatov Institute», 123182 Moscow, Russia
^\squareL. D. Landau Institute for Theoretical Physics RAS, 117940 Moscow, Russia

PACS: 71.10.Pm, 72.10.-d, 73.43.-f
Within the Grassmannian U(2N) / U(N) \times
U(N) non-linear σ model representation of localization one can study the low energy dynamics of both the free and interacting electron gas. We study the cross-over between these two fundamentally different physical problems. We show how the topological arguments for the exact quantization of the Hall conductance are extended to include the Coulomb interaction problem. We discuss dynamical scaling and make contact with the theory of variable range hopping.

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