Some Recent Developments
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Sergio A. Albeverio Raphael J. Høegh-Krohn Sonia Mazzucchi
Mathematical Theory of Feynman Path Integrals An Introduction
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Lecture Notes in Mathematics Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
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Sergio A. Albeverio · Raphael J. Høegh-Krohn Sonia Mazzucchi
Mathematical Theory of Feynman Path Integrals An Introduction 2nd corrected and enlarged edition
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Authors Sergio A. Albeverio Department of Mathematics University of Bonn Wegelerstr. 6 53115 Bonn Germany [email protected]
Sonia Mazzucchi Department of Mathematics University of Trento via Sommarive 14 38050 Povo (TN) Italy [email protected]
Raphael J. Høegh-Krohn University of Oslo Blindern Norway
ISBN: 978-3-540-76954-5 e-ISBN: 978-3-540-76956-9 DOI: 10.1007/978-3-540-76956-9 Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2008921370 Mathematics Subject Classification (2000): 81Q30, 81S40, 28C20, 46Nxx, 46T12, 47D08, 47G30, 60H05, 58D30, 35S30, 41A60, 34E05, 35Q40, 42A38, 81T45 c 2008 Springer-Verlag Berlin Heidelberg ° 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, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH Printed on acid-free paper 987654321 springer.com
Preface to the Second Edition
This second edition, unfortunately, had to be done without the contribution of Raphael Høegh-Krohn, who died on 28 January 1988. The authors of the present edition hope very much that the result of their efforts would had been appreciated by him. His beloved memory has been a steady inspiration to us. Since the appearance of the first edition many new developments have taken place. The present edition tries to take this into account in several ways, keeping however the basic structure and contents of the first edition. At that time the book was the first rigorous one to appear in the area and was written in a sort of pioneering spirit. In our opinion it is still valid as an introduction to all the work which followed; therefore in this second edition we preserve its form entirely (except for correcting some misprints and slightly improving some formulations). A chapter has been however added, in which many new developments are include
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