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Theoretical and Mathematical Physics The series founded in 1975 and formerly (until 2005) entitled Texts and Monographs in Physics (TMP) publishes high-level monographs in theoretical and mathematical physics. The change of title to Theoretical and Mathematical Physics (TMP) signals that the series is a suitable publication platform for both the mathematical and the theoretical physicist. The wider scope of the series is reflected by the composition of the editorial board, comprising both physicists and mathematicians. The books, written in a didactic style and containing a certain amount of elementary background material, bridge the gap between advanced textbooks and research monographs. They can thus serve as basis for advanced studies, not only for lectures and seminars at graduate level, but also for scientists entering a field of research.

Editorial Board W. Beiglböck, Institute of Applied Mathematics, University of Heidelberg, Heidelberg, Germany P. Chrusciel, Gravitational Physics, University of Vienna, Vienna, Austria J.-P. Eckmann, Département de Physique Théorique, Université de Genève, Geneva, Switzerland H. Grosse, Institute of Theoretical Physics, University of Vienna, Vienna, Austria A. Kupiainen, Department of Mathematics, University of Helsinki, Helsinki, Finland H. Löwen, Institute of Theoretical Physics, Heinrich-Heine-University of Duesseldorf, Duesseldorf, Germany M. Loss, School of Mathematics, Georgia Institute of Technology, Atlanta, USA N.A. Nekrasov, IHÉS, Bures-sur-Yvette, France M. Ohya, Tokyo University of Science, Noda, Japan M. Salmhofer, Institute of Theoretical Physics, University of Heidelberg, Heidelberg, Germany S. Smirnov, Mathematics Section, University of Geneva, Geneva, Switzerland L. Takhtajan, Department of Mathematics, Stony Brook University, Stony Brook, USA J. Yngvason, Institute of Theoretical Physics, University of Vienna, Vienna, Austria

For further volumes: www.springer.com/series/720

Monique Combescure r Didier Robert

Coherent States and Applications in Mathematical Physics

Monique Combescure Batiment Paul Dirac IPNL Villeurbanne France

Didier Robert Laboratoire Jean-Leray Departement de Mathematiques Nantes University Nantes Cedex 03 France

ISSN 1864-5879 e-ISSN 1864-5887 Theoretical and Mathematical Physics ISBN 978-94-007-0195-3 e-ISBN 978-94-007-0196-0 DOI 10.1007/978-94-007-0196-0 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2012931507 © Springer Science+Business Media B.V. 2012 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

The main goal of this book i