A Combinatorial Perspective on Quantum Field Theory
This book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author’s biases, through some of the important ways that a combinatorial perspective can be brought to bear on
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Karen Yeats
A Combinatorial Perspective on Quantum Field Theory 123
SpringerBriefs in Mathematical Physics Volume 15
Series editors Nathanaël Berestycki, Cambridge, UK Mihalis Dafermos, Cambridge, UK Tohru Eguchi, Tokyo, Japan Atsuo Kuniba, Tokyo, Japan Matilde Marcolli, Pasadena, USA Bruno Nachtergaele, Davis, USA
More information about this series at http://www.springer.com/series/11953
Karen Yeats
A Combinatorial Perspective on Quantum Field Theory
123
Karen Yeats Department of Mathematics Simon Fraser University Burnaby, BC Canada and Department of Combinatorics and Optimization University of Waterloo Waterloo, ON Canada
ISSN 2197-1757 ISSN 2197-1765 (electronic) SpringerBriefs in Mathematical Physics ISBN 978-3-319-47550-9 ISBN 978-3-319-47551-6 (eBook) DOI 10.1007/978-3-319-47551-6 Library of Congress Control Number: 2016953661 © The Author(s) 2017 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 This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Acknowledgements
I would like to thank all of my colleagues, collaborators, and students, but particularly Dirk Kreimer from whom I learned the keys to this whole area and my students in summer 2016, Iain Crump, Benjamin Moore, Mohamed Laradji, Matthew Lynn, Wesley Chorney, and Maksym Neyra-Nesterenko, who helped proofread this brief. I would also like to thank Cameron Morland for his support.
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Contents
Part I
Preliminaries
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2
Quantum Field Theory Set Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 7
3
Combinatorial Classes and Rooted Trees . . . . . . . . . . . . 3.1 Combinatorial Classes and Augmented Generat
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