The Quantum Theory of Fields Volume I Foundations Steven Weinberg University of Texas at Austin To Louise In The Quantum Theory of Fields Nobel Laureate Steven Weinberg com- bines his exceptional physical insight with his gift for clear exposition to provide a self-contained, comprehensive, and up-to-date introduction to quantum field theory. Volume I introduces the foundations of quantum field theory . The development is fresh and logical throughout, with each step carefully motivated by what has gone before, and emphasizing the reasons why such a theory should describe nature. After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and the properties of particles that follow from these principles. Quantum field theory then emerges from this as a natural consequence. The classic calculations of quantum electrodynamics are presented in a thoroughly modern way, showing the use of path integrals and dimensional regularization. The account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum electrodynamics to ele- mentary particle physics and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research . Problems are included at the end of each chapter . A second volume will describe the modern applications of quantum field theory in today's standard model of elementary particles, and in some areas of condensed matter physics. This will be an invaluable reference work for all physicists and mathe- maticians who use quantum field theory, as well as a textbook appropriate to graduate courses. To Louise The quantum Theory of Fields Volume I Foundations Published by the Press Syndicate of the University of Cambridge The Pitt Building, Trumpington Street, Cambridge C132 I RP 40 West 20th Street, New York, NY 100 11-42 1 1, USA 10 Stamford Road, Oakleigh, Melbourne 3166, Australia Oc Steven Weinberg 1995 First published 1995 Printed in the United States of America A catalogue record fbr this book is available,from the British Library Library ofCongress cataloguing inpublication data Weinberg, Steven, 1933- The quantum theory of fields / Steven Weinberg. p. cm. Includes bibliographical reference and index, Contents: v. 1. Foundations. ISBN 0-521-55(]01-7 1. Quantum field theory. I. Title. Qc174.45.w45 1995 530.1'43-dc20 95-2782 CIP ISBN 0 521 55{101 7 TAG To Louise To Louise Contents Sections marked with an asterisk are somewhat out of the book's main line of development and may be omitted in a first reading . PREFACE xx NOTATION xxv 1 HISTORICAL INTRODUCTION 1 1.1 Relativistic Wave Mechanics De Broglie waves q Schrodinger-Klein-Gordan wave equation q Fine structure q Spin q Dirac equation q Negative energies 0 Exclusion principle q Positrons D Dirac equation reconsidered 1.2 The Birth of Quantum Field Theory 1 5 Born, Heisenberg, Jordan quantized field q Spontaneous emission q Anticom- mutators q Heisenberg-Pauli quantum field theory 0 Furry- -Oppenheimer quan- tization of Dirac field o Pauli- eisskopf quantization of scalar field q Early calculations in quantum electrodynamics q Neutrons q Mesons 1.3 The Problem of Infinities 3 1 Infinite electron energy shifts q Vacuum polarization q Scattering of light by light q 0 Infrared divergences D Search for alternatives Renormalization 0 Shelter Island Conference q Lamb shift q Anomalous electron magnetic moment Schwinger, Tornonaga, Feynman, Dyson formalisms o why not earlier ? Bibliography 39 References 40 2 RELATIVISTIC QUANTUM MECHANICS 49 2.1 Quantum Mechanics 4 9 Rays q Scalar products q Observables q Probabilities Ix