From Classical Field Theory to Perturbative Quantum Field Theory
This book develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying
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Michael Dütsch
From Classical Field Theory to Perturbative Quantum Field Theory
Progress in Mathematical Physics Volume 74
Editors-in-chief Giuseppe Dito, Universite de Bourgogne, Dijon, France Gerald Kaiser, Signals & Waves, Portland, Oregon, USA Michael K.H. Kiessling, The State University of New Jersey, New Jersey, USA Editorial Board Sir M. Berry, University of Bristol, UK P. Blanchard, University of Bielefeld, Germany M. Eastwood, University of Adelaide, Australia A.S. Fokas, University of Cambridge, UK F.W. Hehl, University of Cologne, Germany and University of Missouri-Columbia, USA D. Sternheimer, Université de Bourgogne, Dijon, France C. Tracy, University of California, Davis, USA
More information about this series at http://www.springer.com/series/4813
Michael Dütsch
From Classical Field Theory to Perturbative Quantum Field Theory
Michael Dütsch University of Göttingen Göttingen, Germany
ISSN 1544-9998 ISSN 2197-1846 (electronic) Progress in Mathematical Physics ISBN 978-3-030-04737-5 ISBN 978-3-030-04738-2 (eBook) https://doi.org/10.1007/978-3-030-04738-2 Library of Congress Control Number: 2018968409 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Dedicated to the memory of Raymond Stora and Eberhard Zeidler. Besides H. Epstein and V. Glaser, Raymond Stora is one of the fathers of causal perturbation theory and he passionately worked on this topic until the end of his life [10]. In innumerable discussions with Eberhard Zeidler I learned a lot about the mathematical aspects of quantum field theory and the “unity of mathematics and physics”, and he strongly encouraged me to write this book.
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