Operator Algebras and Quantum Statistical Mechanics C*- and W*-Algeb
In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechani
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w. Beiglbock M. Goldhaber E. H. Lieb W. Thirring Series Editors
ala Bratteli Derek W. Robinson
Operator Algebras and Quantum Statistical Mechanics 1 C*- and W*-Algebras Symmetry Groups Decomposition of States
[I]
Springer Science+Business Media, LLC
Ola Bratteli
Derek W. Robinson
Institute of Mathematics University of Oslo Blindem, Oslo 3 Norway
School of Mathematics University of New South Wales P.O. Box 1 Kensington, NSW Australia 2033
Editors:
Wolf Beiglbock
Maurice Goldhaber
Institut fUr Angewandte Mathematik Universităt Heidelberg Im Neuenheimer Fe1d 5 D-69oo Heidelberg 1 Federal Republic of Germany
Department of Physics Brookhaven National Laboratory Associated Universities, Inc. Upton, NY 11973 USA
Elliott H. Lieb
Walter Thirring
Department of Physics Joseph Henry Laboratories Princeton University P.O. Box 708 Princeton, NJ 08540 USA
Institut fUr Theoretische Physik der Universităt Wien Boltzmanngasse 5 A-I090 Wien Austria
ISBN 978-3-662-02315-0 ISBN 978-3-662-02313-6 (eBook) DOI 10.1007/978-3-662-02313-6 Library of Congress Cataloging in PubIication Data
Bratteli, Ola. Operator algebras and quantum statistical mechanics. (Texts and monographs in physics) Includes bibliographical references and index. 1. Operator algebras. 2. Quantum statistics. 1. Robinson, Derek W., joint author. II. Title. QA326.B74 512'.55 78-27159 AlI rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer-Verlag.
© 1979 by Springer Science+Business Media New York Originally published by Springer-Verlag New York Inc. in 1979 Softcover reprint of the hardcover 1st edition 1979 9876 54321
Preface
In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of development it was realized that this would entail the omission of various interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems offield theory and statistical mechanics. But the theory of 20 years ago was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honeymoon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e.g. asymptotic abelianness and KMS states, new t
