Laurie M. Brown Editor Renormalization From Lorentz to Landau (and Beyond) With 14 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest Laurie M. Brown Department of Physics and Astronomy Northwestern University Evanston, IL 60208 USA Library of Congress Cataloging-in-Publication Data Renormalization: from Lorentz to Landau (and beyond) / edited by Laurie M. Brown. p. cm. Includes bibliographical references. ISBN-13:978-0-387-94401-2 e-ISBN-13:978-1-4612-2720-5 DOl: 10.1007/978-1-4612-2720-5 I. Renormalization (Physics)-History. I. Brown, Laurie M. QC174.l7.R46R46 1993 530.l'43-dc20 92-32376 Printed on acid-free paper. © 1993 Springer-Verlag New York Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may according be used freely by anyone. Production managed by Bill Imbornoni; manufacturing supervised by Jacqui Ashri. Typeset by Asco Trade Typesetting Ltd., Hong Kong. 9 8 7 6 5 4 3 2 1 ISBN-13:978-0-387-9440I-2 Contents Contributors Vll Introduction: Renormalization. 1930-1950 Laurie M. Brown 1.1. Apologia.............................................. 3 1.2. Quantum Electrodynamics: 1926-1930 .................... 4 1.3. The Decade of Struggle: 1930-1940 ....................... 8 1.4. The Triumph of Renormalization: The 1940s ............... 13 2 Renormalization in Historical Perspective-The First Stage 29 Max Dresden 2.1. Renormalization: The Disappearance and Reappearance of an Idea ............................................. 31 2.2. J. J. Thompson: The Aether as Fluid and the Electromagnetic Mass ................................... 36 2.3. Lorentz: His Aether, Electron, and Program ................ 41 2.4. Kramers: The Unexpected End of the First Phase ........... 47 2.5. Comments and Conclusions .............................. 53 3 Tutorial on Infinities in QED 57 Robert Mills 3.1. Introduction........................................... 59 3.2. Subtracting Infinity ..................................... 61 3.3. The Perturbation Expansion ............................. 63 3.4. Feynman Graphs ....................................... 67 3.5. Self-Energy Graphs and Vertex Graphs .................... 74 3.6. Primitive Renormalization ............................... 78 3.7. The Renormalization Program ........................... 80 3.8. Discussion ............................................ 84 v vi Contents 4 New Philosophy of Renormalization: From the Renormalization Group Equations to Effective Field Theories 87 Tian Yu Cao 4.1. Conceptual Background ................................. 89 4.1.1. The Locality Assumption. 90 4.1.2. The Operator Field Assumption .................... 91 4.1.3. The Plenum Assumption ofthe Vacuum ............. 92 4.1.4. Renormalization and the Consistency ofQFT ........ 92 4.2. Foundational Transformations ........................... 103 4.2.1. Cutoff.......................................... 103 4.2.2. Symmetry and Symmetry Breaking ................. 107 4.2.3. Scale Invariance and Renormalization Group Approach 109 4.2.4. Decoupling Theorem and Effective Field Theories ..... 116 4.3. New Philosophy ....................................... 118 5 Changing Conceptualization of Renormalization Theory 135 Silvan S. Schweber 5.1. Introduction........................................... 137 5.2. The History of Quantum Mechanics and QFT .............. 138 5.3. The Post-World War II Developments .................... 143 5.4. The Changing Conceptualization of Renormalization. Effective Field Theories ......................................... 150 5.5. The Ebb and Flow of Reductionism ....................... 155 Appendix Historical Remarks on the Renormalization Group 167 Dmitri V. Shirkov A.1. History of RG in Quantum Field Theory .................. 169 A.1.1. Renormalization and Renormalization Invariance .... 169 A.1.2. The Birth of the Renormalization Group ........... 170 A.1.3. Creation of the RG Method in the Mid-1950s ....... 172 A.1.4. Other Early Applications ofRG ................... 174 A.1.5. Further Development ofRG in QFT ............... 175 A.2. RG in Critical Phenomena and Other Fields ............... 176 A.2.1. Spin Lattices ................................... 176 A.2.2. Turbulence .................................... 177 A.2.3. Paths of RG Expansion .......................... 178 A.2.4. Two Faces of RG in QFT ........................ 179 A.2.5. Functional Self-Similarity or Synthesis ............. 181 A.3. Summary ............................................ 182 Name Index 187 Contributors Laurie M. Brown Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA Tian Yu Cao Dibner Institute for the History of Science and Technology, Massachu­ setts Institute of Technology, Cambridge, MA 02139, USA Max Dresden Stanford Linear Accelerator Center, Stanford, CA 94309, USA, and Program of the History of Physics, Stanford University, Stanford, CA 94309, USA Robert Mills Department of Physics, Ohio State University, Columbus, OH 43210, USA Silvan S. Schweber Department of Physics, Brandeis University, Waltham, MA 02154, USA Dmitri V. Shirkov Laboratory for Theoretical Physics, Joint Institute for Nuclear Re­ search, Dubna, Russia, and Ludwig-Maximilian-UniversiHit, Munchen, Germany vii .