Advanced Quantum Mechanics

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Renowned physicist and mathematician Freeman Dyson is famous for his work in quantum mechanics, nuclear weapons policy and bold visions for the future of humanity. In the 1940s, he was responsible for demonstrating the equivalence of the two formulations of quantum electrodynamics - Richard Feynman's diagrammatic path integral formulation and the variational methods developed by Julian Schwinger and Sin-Itiro Tomonoga - showing the mathematical consistency of QED.

This invaluable volume comprises the legendary, never-before-published, lectures on quantum electrodynamics first given by Dyson at Cornell University in 1951. The late theorist Edwin Thompson Jaynes once remarked "For a generation of physicists they were the happy medium: clearer and motivated than Feynman, and getting to the point faster than Schwinger".

Future generations of physicists are bound to read these lectures with pleasure, benefiting from the lucid style that is so characteristic of Dyson's exposition.
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Product Details

  • ISBN-13: 9789812706614
  • Publisher: World Scientific Publishing Company, Incorporated
  • Publication date: 5/28/2007
  • Edition description: Older Edition
  • Pages: 220
  • Product dimensions: 6.50 (w) x 9.60 (h) x 0.70 (d)

Table of Contents

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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