Perturbative Algebraic Quantum Field Theory An Introduction for Math
Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities. We discuss in detail the e
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Kasia Rejzner
Perturbative Algebraic Quantum Field Theory An Introduction for Mathematicians
Mathematical Physics Studies Series editors Giuseppe Dito, Dijon, France Edward Frenkel, Berkeley, CA, USA Sergei Gukov, Pasadena, CA, USA Yasuyuki Kawahigashi, Tokyo, Japan Maxim Kontsevich, Bures-sur-Yvette, France Nicolaas P. Landsman, Nijmegen, The Netherlands
More information about this series at http://www.springer.com/series/6316
Kasia Rejzner
Perturbative Algebraic Quantum Field Theory An Introduction for Mathematicians
123
Kasia Rejzner Department of Mathematics University of York York UK
ISSN 0921-3767 Mathematical Physics Studies ISBN 978-3-319-25899-7 DOI 10.1007/978-3-319-25901-7
ISSN 2352-3905
(electronic)
ISBN 978-3-319-25901-7
(eBook)
Library of Congress Control Number: 2015953254 Springer Cham Heidelberg New York Dordrecht London © The Author(s) 2016 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. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
This book is dedicated to the memory of Rudolf Haag, Daniel Kastler, Uffe Haagerup, Raymond Stora and John Roberts, who passed away recently.
Acknowledgements
I would like to thank my friends and collaborators for enlightening discussions and continuous support that made this book possible. In particular I would like to mention Susama Agarwala, Dorothea Bahns, Christian Brouder, Yoann Dabrowski, Nguyen Viet Dang, Chris Fewster, Alessandra Frabetti, Klaus Fredenhagen, Frédéric Hélein, Eli Hawkins (thanks for your engagement and time commitment!), Camille Laurent-Gengoux, Dominique Manchon and Pedro Lauridsen-Ribeiro. York, UK
Kasia Rejzner
vii
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2 Algebraic Approach to Quantum Theory . . . . . 2.1 Algebraic Quantum Mechanics . . . . . . . . . . 2.1.1 Functional Analytic Preliminaries . . . 2.1.2 Observables and
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