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Preface v
Generally used Notation xiii
Introduction 1
Books 1
Subject Matter 1
Detailed Program 2
One-Particle Theories 3
The Dirac Theory 5
The Form of the Dirac Equation 5
Lorentz Invariance of the Dirac Equation 7
To Find the S 9
The Covariant Notation 11
Conservation Laws. Existence of Spin 12
Elementary Solutions 13
The Hole Theory 14
Positron States 15
Electromagnetic Properties of the Electron 16
The Hydrogen Atom 18
Solution of Radial Equation 20
Behaviour of an Electron in a Non-Relativistic Approximation 23
Summary of Matrices in the Dirac Theory in Our Notation 26
Summary of Matrices in the Dirac Theory in the Feynman Notation 28
Scattering Problems and Born Approximation 31
General Discussion 31
Projection Operators 32
Calculation of Traces 34
Scattering of Two Electrons in Born Approximation. The Moller Formula 39
Relation ofCross-sections to Transition Amplitudes 41
Results for Moller Scattering 43
Note on the Treatment of Exchange Effects 44
Relativistic Treatment of Several Particles 45
Field Theory 47
Classical Relativistic Field Theory 47
Quantum Relativistic Field Theory 51
The Feynman Method of Quantization 52
The Schwinger Action Principle 53
The Field Equations 55
The Schrodinger Equation for the State-function 55
Operator Form of the Schwinger Principle 56
The Canonical Commutation Laws 57
The Heisenberg Equation of Motion for the Operators 58
General Covariant Commutation Laws 58
Anticommuting Fields 59
Examples of Quantized Field Theories 61
The Maxwell Field 61
Momentum Representations 63
Fourier Analysis of Operators 65
Emission and Absorption Operators 65
Gauge-Invariance of the Theory 67
The Vacuum State 68
The Gupta-Bleuler Method 70
Example: Spontaneous Emission of Radiation 71
The Hamiltonian Operator 74
Fluctuations of the Fields 75
Fluctuation of Position of an Electron in a Quantized Electromagnetic Field. The Lamb Shift 77
Theory of Line Shift and Line Width 79
The Interaction Representation 80
The Application of the Interaction Representation to the Theory of Line-Shift and Line-Width 82
Calculation of Line-Shift, Non-Relativistic Theory 87
The Idea of Mass Renormalization 88
Field Theory of the Dirac Electron, Without Interaction 91
Covariant Commutation Rules 92
Momentum Representations 94
Fourier Analysis of Operators 94
Emission and Absorption Operators 95
Charge-Symmetrical Representation 96
The Hamiltonian 97
Failure of Theory with Commuting Fields 98
The Exclusion Principle 98
The Vacuum State 99
Field Theory of Dirac Electron in External Field 100
Covariant Commutation Rules 101
The Hamiltonian 104
Antisymmetry of the States 105
Polarization of the Vacuum 106
Calculation of Momentum Integrals 111
Physical Meaning of the Vacuum Polarization 115
Vacuum Polarization for Slowly Varying Weak Fields. The Uehling Effect 119
Field Theory of Dirac and Maxwell Fields in Interaction 120
The Complete Relativistic Quantum Electrodynamics 120
Free Interaction Representation 122
Free Particle Scattering Problems 125
Moller Scattering of Two Electrons 126
Properties of the D[subscript F] Function 128
The Moller Formula, Conclusion 129
Electron-Positron Scattering 130
Scattering of a Photon by an Electron. The Compton Effect. Klein-Nishina Formula 130
Calculation of the Cross-Section 133
Sum Over Spins 134
Two Quantum Pair Annihilation 139
Bremsstrahlung and Pair Creation in the Coulomb Field of an Atom 142
General Theory of Free Particle Scattering 145
The Reduction of an Operator to Normal Form 148
Feynman Graphs 152
Feynman Rules of Calculation 155
The Self-Energy of the Electron 158
Second-Order Radiative Corrections to Scattering 162
The Treatment of Low-Frequency Photons. The Infra-Red Catastrophe 181
Scattering by a Static Potential. Comparison with Experimental Results 183
The Magnetic Moment of the Electron 189
Relativistic Calculation of the Lamb Shift 191
Covariant Part of the Calculation 193
Covariant Part of the Calculation 193
Discussion and the Nature of the [Omega]-Representation 196
Concluding Non-Covariant Part of the Calculation 198
Accuracy of the Lamb Shift Calculation 202
Notes 205
References 210
Index 215
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