Progress in Mathematical Physics Volume 45
Editors-in-Chief Anne Boutet de Monvel, Université Paris VII Denis Diderot, France Gerald Kaiser, Center for Signals and Waves, Austin, TX, USA
Editorial Board Sir M. Berry, University of Bristol, UK C. Berenstein, University of Maryland, College Park, USA P. Blanchard, University of Bielefeld, Germany A.S. Fokas, University of Cambridge, UK D. Sternheimer, Université de Bourgogne, Dijon, France C. Tracy, University of California, Davis, USA
The Quantum Hall Effect Poincaré Seminar 2004
Benoît Douçot Bertrand Duplantier Vincent Pasquier Vincent Rivasseau Editors
Birkhäuser Verlag Basel • Boston • Berlin
Editors: Benoît Douçot LPTHE CNRS et Universités Paris 6 et 7 Tour 24-14 5e étage 4 place Jussieu F-75252 Paris Cedex 05 e-mail:
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Bertrand Duplantier Service de Physique Théorique Orme des Merisiers CEA – Saclay F-91191 Gif-sur-Yvette Cedex e-mail:
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Vincent Pasquier Service de Physique Théorique Orme des Merisiers CEA – Saclay F-91191 Gif sur Yvette Cedex e-mail:
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Vincent Rivasseau Laboratoire de Physique Théorique Université Paris XI F-91405 Orsay Cedex e-mail:
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2000 Mathematics Subject Classification 81V70
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at .
ISBN 3-7643-7300-8 Birkhäuser Verlag, Basel – Boston – Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use whatsoever, permission from the copyright owner must be obtained. © 2005 Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced of chlorine-free pulp. TCF ' Printed in Germany ISBN-10: 3-7643-7300-8 ISBN-13: 978-3-7643-7300-9 987654321
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Contents Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .