Advanced Quantum Mechanics

by Dyson, Freeman; Derbes, David (CON)

• ISBN13: 9789812706225
• ISBN10: 9812706224
• Format: Hardcover
• Copyright: 2007-03-12
• Publisher: World Scientific Pub Co Inc

Summary

From his early years as a student in Trinity College, Cambridge, to his studies with Hans Bethe at Cornell University, Freeman Dyson has proven himself to be the best mathematician from England and the best English physicist since Dirac. In the fateful year 1949, Dyson published two ground-breaking papers in the Physical Review, The radiation theories of Tomonaga, Schwinger, and Feynman and The S matrix in quantum electrodynamics. The first demonstrated the equivalence of the Schwinger-Tomonaga approach and the Feynman path integral method in quantum electrodynamics. The second crystalized the Feynman rules for scattering diagrams. Here for the first time, Dyson's lectures at Cornell University shortly after, in 1951, are presented. Brimming with youthful vigour and excitement from the golden years of QED, highly original in their approach, the student is taken for a thrilling ride through the Dirac equation, its manifold consequences, to field theory, the Dyson graphs, and finally to the Feynman diagrams. Book jacket.

Author Biography

Freeman Dyson is Professor Emeritus at the Institute for Advanced Study in Princeton.

Table of Contents

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