Advanced quantum mechanics

Contents......Page 9
Preface......Page 6
Generally used Notation......Page 13
1.2 Subject Matter......Page 14
1.3 Detailed Program......Page 15
1.4 One-Particle Theories......Page 16
2.1 The Form of the Dirac Equation......Page 18
2.2 Lorentz Invariance of the Dirac Equation......Page 20
2.3 To Find the S......Page 22
2.4 The Covariant Notation......Page 24
2.5 Conservation Laws. Existence of Spin......Page 25
2.6 Elementary Solutions......Page 26
2.7 The Hole Theory......Page 27
2.8 Positron States......Page 28
2.9 Electromagnetic Properties of the Electron......Page 29
2.10 The Hydrogen Atom......Page 31
2.11 Solution of Radial Equation......Page 33
2.12 Behaviour of an Electron in a Non-Relativistic Approximation......Page 36
2.13 Summary of Matrices in the Dirac Theory in Our Notation......Page 39
2.14 Summary of Matrices in the Dirac Theory in the Feynman Notation......Page 41
3.1 General Discussion......Page 44
3.2 Projection Operators......Page 45
3.3 Calculation of Traces......Page 47
3.4 Scattering of Two Electrons in Born Approximation. The Moller Formula......Page 52
3.5 Relation of Cross-sections to Transition Amplitudes......Page 54
3.6 Results for Moller Scattering......Page 56
3.7 Note on the Treatment of Exchange Effects......Page 57
3.8 Relativistic Treatment of Several Particles......Page 58
4.1 Classical Relativistic Field Theory......Page 60
4.2 Quantum Relativistic Field Theory......Page 64
4.3 The Feynman Method of Quantization......Page 65
4.4 The Schwinger Action Principle......Page 66
4.4.2 The Schrodinger Equation for the State-function......Page 68
4.4.3 Operator Form of the Schwinger Principle......Page 69
4.4.4 The Canonical Commutation Laws......Page 70
4.4.6 General Covariant Commutation Laws......Page 71
4.4.7 Anticommuting Fields......Page 72
5.1 The Maxwell Field......Page 74
5.1.1 Momentum Representations......Page 76
5.1.3 Emission and Absorption Operators......Page 78
5.1.4 Gauge-Invariance of the Theory......Page 80
5.1.5 The Vacuum State......Page 81
5.1.6 The Gupta-Bleuler Method......Page 83
5.1.7 Example: Spontaneous Emission of Radiation......Page 84
5.1.8 The Hamiltonian Operator......Page 87
5.1.9 Fluctuations of the Fields......Page 88
5.1.10 Fluctuation of Position of an Electron in a Quantized Electromagnetic Field. The Lamb Shift......Page 90
5.2 Theory of Line Shift and Line Width......Page 92
5.2.1 The Interaction Representation......Page 93
5.2.2 The Application of the Interaction Representation to the Theory of Line-Shift and Line-Width......Page 95
5.2.3 Calculation of Line-Shift, Non-Relativistic Theory......Page 100
5.2.4 The Idea of Mass Renormalization......Page 101
5.3 Field Theory of the Dirac Electron, Without Interaction......Page 104
5.3.1 Covariant Commutation Rules......Page 105
5.3.3 Fourier Analysis of Operators......Page 107
5.3.4 Emission and Absorption Operators......Page 108
5.3.5 Charge-Symmetrical Representation......Page 109
5.3.6 The Hamiltonian......Page 110
5.3.8 The Exclusion Principle......Page 111
5.3.9 The Vacuum State......Page 112
5.4 Field Theory of Dirac Electron in External Field......Page 113
5.4.1 Covariant Commutation Rules......Page 114
5.4.2 The Hamiltonian......Page 117
5.4.3 Antisymmetry of the States......Page 118
5.4.4 Polarization of the Vacuum......Page 119
5.4.5 Calculation of Momentum Integrals......Page 124
5.4.6 Physical Meaning of the Vacuum Polarization......Page 128
5.4.7 Vacuum Polarization for Slowly Varying Weak Fields. The Uehling Effect......Page 132
5.5.1 The Complete Relativistic Quantum Electrodynamics......Page 133
5.5.2 Free Interaction Representation......Page 135
6 Free Particle Scattering Problems......Page 138
6.1 Moller Scattering of Two Electrons......Page 139
6.1.1 Properties of the DF Function......Page 141
6.1.2 The Moller Formula, Conclusion......Page 142
6.2 Scattering of a Photon by an Electron. The Compton Effect Klein-Nishina Formula......Page 143
6.2.1 Calculation of the Cross-Section......Page 146
6.2.2 Sum Over Spins......Page 147
6.3 Two Quantum Pair Annihilation......Page 152
6.4 Bremsstrahlung and Pair Creation in the Coulomb Field of an Atom......Page 155
7 General Theory of Free Particle Scattering......Page 158
7.1 The Reduction of an Operator to Normal Form......Page 161
7.2 Feynman Graphs......Page 165
7.3 Feynman Rules of Calculation......Page 168
7.4 The Self-Energy of the Electron......Page 171
7.5 Second-Order Radiative Corrections to Scattering......Page 175
7.6 The Treatment of Low-Frequency Photons. The Infra-Red Catastrophe......Page 194
8 Scattering by a Static Potential. Comparison with Experimental Results......Page 196
8.1 The Magnetic Moment of the Electron......Page 202
8.2 Relativistic Calculation of the Lamb Shift......Page 204
8.2.1 Covariant Part of the Calculation......Page 206
8.2.2 Discussion and the Nature of the  -Representation......Page 209
8.2.3 Concluding Non-Covariant Part of the Calculation......Page 211
8.2.4 Accuracy of the Lamb Shift Calculation......Page 215
Notes......Page 218
References......Page 224
Index......Page 228