The Quantum Theory of Fields (Volume 1)

638 Pages·1995·27.69 MB·English

by  Steven Weinberg

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