Quantum Many Body Systems Cetraro, Italy 2010, Editors: Alessandro

The book is based on the lectures given at the CIME school "Quantum many body systems" held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written by four leading experts in the fie

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Fondazione C.I.M.E., Firenze C.I.M.E. stands for Centro Internazionale Matematico Estivo, that is, International Mathematical Summer Centre. Conceived in the early fifties, it was born in 1954 in Florence, Italy, and welcomed by the world mathematical community: it continues successfully, year for year, to this day. Many mathematicians from all over the world have been involved in a way or another in C.I.M.E.’s activities over the years. The main purpose and mode of functioning of the Centre may be summarised as follows: every year, during the summer, sessions on different themes from pure and applied mathematics are offered by application to mathematicians from all countries. A Session is generally based on three or four main courses given by specialists of international renown, plus a certain number of seminars, and is held in an attractive rural location in Italy. The aim of a C.I.M.E. session is to bring to the attention of younger researchers the origins, development, and perspectives of some very active branch of mathematical research. The topics of the courses are generally of international resonance. The full immersion atmosphere of the courses and the daily exchange among participants are thus an initiation to international collaboration in mathematical research. C.I.M.E. Director Pietro ZECCA Dipartimento di Energetica “S. Stecco” Universit`a di Firenze Via S. Marta, 3 50139 Florence Italy e-mail: [email protected]

C.I.M.E. Secretary Elvira MASCOLO Dipartimento di Matematica “U. Dini” Universit`a di Firenze viale G.B. Morgagni 67/A 50134 Florence Italy e-mail: [email protected]

For more information see CIME’s homepage: http://www.cime.unifi.it CIME activity is carried out with the collaboration and financial support of: - INdAM (Istituto Nazionale di Alta Matematica) - MIUR (Ministero dell’Universit´a e della Ricerca) This course is partially supported by GDR-GDRE on CONTROLE DES EQUATIONS AUX DERIVEES PARTIELLES (CONEDP).

Vincent Rivasseau Jan Philip Solovej

 

Robert Seiringer Thomas Spencer

Quantum Many Body Systems Cetraro, Italy 2010 Editors: Alessandro Giuliani Vieri Mastropietro Jakob Yngvason

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Vincent Rivasseau Universit´e Paris-Sud Laboratoire de Physique Th´eorique Orsay, France

Jan Philip Solovej Department of Mathematics University of Copenhagen Copenhagen, Denmark

Robert Seiringer McGill University Department of Mathematics and Statistics Montreal, QC, Canada

Thomas Spencer Institute for Advanced Study School of Mathematics Princeton, NJ, USA

ISBN 978-3-642-29510-2 ISBN 978-3-642-29511-9 (eBook) DOI 10.1007/978-3-642-29511-9 Springer Heidelberg New York Dordrecht London Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2012941621 Mathematics Subject Classification (2010): 82B10, 81V70, 82B28, 82B44 c Springer-Verlag Berlin Heidelberg 2012  This work is subject to copyright. All rights are reserved by the Publisher, whether the whol