Relativistic Quantum Mechanics And Field Theory

647 Pages·1993·32.943 MB·English

by  Franz Gross

RELATIVISTIC
QUANTUM MECHANICS
AND FIELD THEORY
RELATIVISTIC
QUANTUM MECHANICS
AND FIELD THEORY
FRANZ GROSS
CollegeofWilliamand Mary
Williamsburg,Virginia
and
Continuous Electron Beam Accelerator Facility
Newport News,Virgina
A Wiley-Interscience Publication
JOHN WILEY It SONS, INC.
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LibraryofCongress CataloginginPublicationData:
Gross, Franz
Relativisticquantummechanicsand fieldtheorylFranzGross.
p. em.
Includes index.
ISBN 0-471-59113-0
1. Relativisticquantumtheory. 2. Quantumfieldtheory.
3. Symmetry(Physics)4. Gauge fields(Physics) I.Title.
QCI74.24.R4G76 1993
530.1'2---dc20 92-40605
Printedinthe United States ofAmerica
10 9 8 7 6 5 4 3 2 1
Tomy parents, Genevieve and Llewellyn
and to the next generation, Glen, Sue, Kathy, Caitlin, and Christina

CONTENTS
Preface xiii
Part I QUANTUM THEORY OF RADIATION 1
1. Quantization of the Nonrelativistic String 3
1.1 The one-dimensional classical string 3
1.2 Normal modes of the string 7
1.3 Quantization of the string 10
1.4 Canonical commutation relations 12
1.5 The number operator and phonon states 13
1.6 The quanta as particles 15
1.7 The classical limit: Field-particle duality 18
1.8 Time translation 22
Problems 25
2. Quantization of the Electromagnetic Field 28
2.1 Lorentz transformations 28
2.2 Relativistic form of Maxwell's theory 31
2.3 Interactions between particles and fields 39
2.4 Plane wave expansions 42
2.5 Massive vector fields 44
2.6 Field quantization 46
2.7 Spin of the photon 50
Problems 56
3. Interaction of Radiation with Matter 57
3.1 Time evolution and the S-matrix 57
3.2 Decay rates and cross sections 65
vii
viii CONTENTS
3.3 Atomic decay 69
3.4 The Lamb shift 73
3.5 Deuteron photodisintegration 81
Problems 85
Part II RELATIVISTIC EQUATIONS 89
4. The Klein-Gordon Equation 91
4.1 The equation 91
4.2 Conserved norm 94
4.3 Solutions for free particles 95
4.4 Pair creation from a high Coulomb barrier 97
4.5 Two-component form 102
4.6 Nonrelativistic limit 106
4.7 Coulomb scattering 108
4.8 Negative energy states 110
Problems 116
5. The Dirac Equation 119
5.1 The equation 119
5.2 Conserved norm 122
5.3 Solutions for free particles 123
5.4 Charge conjugation 126
5.5 Coulomb scattering 129
5.6 Negative energy states 131
5.7 Nonrelativistic limit 134
5.8 The Lorentz group 140
5.9 Covariance of the Dirac equation 146
5.10 Bilinearcovariants 152
5.11 Chirality and massless fermions 157
Problems 169
6. Application of the Dirac Equation 163
6.1 Spherically symmetric potentials 163
6.2 Hadronic structure 171
6.3 Hydrogen-like atoms 177
Problems 183
CONTENTS ix
Part III ELEMENTS OF QUANTUM FIELD THEORY 185
7. Second Quantization 187
7.1 Schrodinger theory 188
7.2 Identical particles 191
7.3 Charged Klein-Gordon theory 194
7.4 Dirac theory 198
7.5 Interactions: An introduction 201
Problems 204
8. Symmetries I 206
8.1 Noether's theorem 206
8.2 Translations 212
8.3 Transformations of states and operators 214
8.4 Parity 216.
8.5 Charge conjugation 219
8.6 Time reversal 223
8.7 The POT theorem 231
Problems 236
9. Interacting Field Theories 238
9.1 ¢3 theory: An example 238
9.2 Relativistic decays 240
9.3 Relativistic scattering 243
9.4 Introduction to the Feynman rules 247
9.5 Calculation of the cross section 252
9.6 Effective nonrelativistic potential 257
9.7 Identical particles 258
9.8 Pion-nucleon interactions and isospin 264
9.9 One-pion exchange 268
9.10 Electroweak decays 273
Problems 279
10. Quantum Electrodynamics 282
10.1 The Hamiltonian 282
10.2 Photon propagator: ep scattering 286
10.3 Antiparticles: e+e- ~ uru: 296