Quantum Field Theory: A Modern Perspective

Graduate Texts in Contemporary Physics Series Editors: R. Stephen Berry Joseph L. Birman Mark P. Silverman H. Eugene Stanley Mikhail Voloshin V. Parameswaran Nair Quantum Field Theory A Modern Perspective With 100 Illustrations V. Parameswaran Nair Physics Department City College Convent Avenue & 138th Street New York, NY 10031 USA Series Editors R. Stephen Berry Department of Chemistry University of Chicago Chicago, IL 60637 USA Joseph L. Birman Department of Physics City College of CUNY New York, NY 10031 USA H. Eugene Stanley Center for Polymer Studies Physics Department Boston University Boston, MA 02215 USA Mikhail Voloshin Theoretical Physics Institute Tate Laboratory of Physics The University of Minnesota Minneapolis, MN 55455 USA Mark P. Silverman Department of Physics Trinity College Hartford, CT 06106 USA On the cover: The pinching contribution to the interaction between fermions. See page 213 for discussion. Library of Congress Cataloging-in-Publication Data Nair, V. P. Topics in quantum field theory / V.P. Nair. p. cm. Includes bibliographical references and index. ISBN 0-387-21386-4 (alk. paper) 1. Quantum field theory. I. Title. QC174.45.N32 2004 530.14′3—dc22 ISBN 0-387-21386-4 2004049910 Printed on acid-free paper. © 2005 Springer Science+Business Media, 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 Science+Business Media, Inc., 233 Spring Street, New York, NY 10013, 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 in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 9 8 7 6 5 4 3 2 1 springeronline.com (MVY) SPIN 10955741 To the memory of my parents Velayudhan and Gowrikutty Nair Preface Quantum field theory, which started with Dirac’s work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for quantum gravity. This also means that quantum field theory has by now evolved into such a vast subject, with many subtopics and many ramifications, that it is impossible for any book to capture much of it within a reasonable length. While there is a common core set of topics, every book on field theory is ultimately illustrating facets of the subject which the author finds interesting and fascinating. This book is no exception; it presents my view of certain topics in field theory loosely knit together and it grew out of courses on field theory and particle phy