Coherent States, Wavelets, and Their Generalizations
This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wa
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Syed Twareque Ali Jean-Pierre Antoine Jean-Pierre Gazeau
Coherent States, Wavelets, and Their Generalizations Second Edition
Coherent States, Wavelets, and Their Generalizations
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 Genéve, 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 Düsseldorf, Düsseldorf, 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: http://www.springer.com/series/720
Syed Twareque Ali • Jean-Pierre Antoine Jean-Pierre Gazeau
Coherent States, Wavelets, and Their Generalizations Second Edition
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Syed Twareque Ali Department of Mathematics and Statistics Concordia University Montréal, Québec Canada
Jean-Pierre Antoine Institut de Recherche en Mathématique et Physique (IRMP) Université Catholique de Louvain Louvain-la-Neuve, Belgium
Jean-Pierre Gazeau Astroparticules et Cosmologie (APC, UMR 7164) Université Paris Diderot, Sorbonne Paris Cité Paris, France Centro Brasileiro de Pesquisas Fisicas (CBPF) Rio de Janeiro, Brasil
ISSN 1864-5879 ISSN 1864-5887 (electronic) ISBN 978-1-4614-8534-6 ISBN 978-1-4614-8535-3 (eBook) DOI 10.1007/978-1-4614-8535-3 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2013947161 © Springer Science+Business Media New York 1999, 2014 This work is subject to copyright. All rights are reserved by the
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