Advanced Quantum Mechanics (Second Edition)

by Freeman Dyson, David Derbes (Translator)

Overview

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 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 better motivated than Feynman, and getting to the point faster than Schwinger”.This edition has been printed on the 60th anniversary of the Cornell lectures, and includes a foreword by science historian David Kaiser, as well as notes from Dyson's lectures at the Les Houches Summer School of Theoretical Physics in 1954. The Les Houches lectures, described as a supplement to the original Cornell notes, provide a more detailed look at field theory, a careful and rigorous derivation of Fermi's Golden Rule, and a masterful treatment of renormalization and Ward's Identity.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.

Product Details

ISBN-13:	9789814383417
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	11/28/2011
Edition description:	New Edition
Pages:	316
Product dimensions:	6.40(w) x 9.70(h) x 0.80(d)

Table of Contents

Foreword v

Preface xiii

Preface to First Edition xvii

Generally used Notation xxv

1 Introduction 1

1.1 Books 1

1.2 Subject Matter 1

1.3 Detailed Program 2

1.4 One-Particle Theories 3

2 The Dirac Theory 5

2.1 The Form of the Dirac Equation 5

2.2 Lorentz Invariance of the Dirac Equation 7

2.3 To Find the S 9

2.4 The Covariant Notation 11

2.5 Conservation Laws. Existence of Spin 12

2.6 Elementary Solutions 13

2.7 The Hole Theory 14

2.8 Positron States 15

2.9 Electromagnetic Properties of the Electron 16

2.10 The Hydrogen Atom 18

2.11 Solution of Radial Equation 20

2.12 Behaviour of an Electron in a Non-Relativistic Approximation 23

2.13 Summary of Matrices in the Dirac Theory in Our Notation 26

2.14 Summary of Matrices in the Dirac Theory in the Feynman Notation 28

Scattering Problems and Born Approximation 31

3.1 General Discussion 31

3.2 Projection Operators 32

3.3 Calculation of Traces 34

3.4 Scattering of Two Electrons in Born Approximation. The Møller Formula 39

3.5 Relation of Cross-sections to Transition Amplitudes 41

3.6 Results for Møller Scattering 43

3.7 Note on the Treatment of Exchange Effects 44

3.8 Relativistic Treatment of Several Particles 45

4 Field Theory 47

4.1 Classical Relativistic Field Theory 47

4.2 Quantum Relativistic Field Theory 51

4.3 The Feynman Method of Quantization 52

4.4 The Schwinger Action Principle 53

4.4.1 The Field Equations 55

4.4.2 The Schrodinger Equation for the State-function 55

4.4.3 Operator Form of the Schwinger Principle 56

4.4.4 The Canonical Commutation Laws 57

4.4.5 The Heisenberg Equation of Motion for the Operators 58

4.4.6 General Covariant Commutation Laws 58

4.4.7 Anticommuting Fields 59

5 Examples of Quantized Field Theories 61

5.1 The Maxwell Field 61

5.1.1 Momentum Representations 63

5.1.2 Fourier Analysis of Operators 65

5.1.3 Emission and Absorption Operators 65

5.1.4 Gauge-Invariance of the Theory 67

5.1.5 The Vacuum State 68

5.1.6 The Gupta-Bleuler Method 70

5.1.7 Example: Spontaneous Emission of Radiation 71

5.1.8 The Hamiltonian Operator 74

5.1.9 Fluctuations of the Fields 75

5.1.10 Fluctuation of Position of an Electron in a Quantized Electromagnetic Field. The Lamb Shift 77

5.2 Theory of Line Shift and Line Width 79

5.2.1 The Interaction Representation 80

5.2.2 The Application of the Interaction Representation, to the Theory of Line-Shift and Line-Width 82

5.2.3 Calculation of Line-Shift, Non-Relativistic Theory 87

5.2.4 The Idea of Mass Renormalization 88

5.3 Field Theory of the Dirac Electron, Without Interaction 91

5.3.1 Covariant Commutation Rules 92

5.3.2 Momentum Representations 94

5.3.3 Fourier Analysis of Operators 94

5.3.4 Emission and Absorption Operators 95

5.3.5 Charge-Symmetrical Representation 96

5.3.6 The Hamiltonian 97

5.3.7 Failure of Theory with Commuting Fields 98

5.3.8 The Exclusion Principle 98

5.3.9 The Vacuum State 99

5.4 Field Theory of Dirac Electron in External Field 100

5.4.1 Covariant Commutation Rules 101

5.4.2 The Hamiltonian 104

5.4.3 Antisymmetry of the States 105

5.4.4 Polarization of the Vacuum 106

5.4.5 Calculation of Momentum Integrals 111

5.4.6 Physical Meaning of the Vacuum Polarization 115

5.4.7 Vacuum Polarization for Slowly Varying Weak Fields. The Uehling Effect 119

5.5 Field Theory of Dirac and Maxwell Fields in Interaction 120

5.5.1 The Complete Relativistic Quantum Electrodynamics 120

5.5.2 Free Interaction Representation 122

6 Free Particle Scattering Problems 125

6.1 Møller Scattering of Two Electrons 126

6.1.1 Properties of the D_F Function 128

6.1.2 The Møller Formula, Conclusion 129

6.1.3 Electron-Positron Scattering 130

6.2 Scattering of a Photon by an Electron. The Compton Effect, Klein-Nishina Formula 130

6.2.1 Calculation of the Cross-Section 133

6.2.2 Sum Over Spins 134

6.3 Two Quantum Pair Annihilation 139

6.4 Bremsstrahlung and Pair Creation in the Coulomb Field of an Atom 142

7 General Theory of Free Particle Scattering 145

7.1 The Reduction of an Operator to Normal Form 148

7.2 Feynman Graphs 152

7.3 Feynman Rules of Calculation 155

7.4 The Self-Energy of the Electron 158

7.5 Second-Order Radiative Corrections to Scattering 162

7.6 The Treatment of Low-Frequency Photons. The Infra-Red Catastrophe 181

8 Scattering by a Static Potential. Comparison with Experimental Results 183

8.1 The Magnetic Moment of the Electron 189

8.2 Relativistic Calculation of the Lamb Shift 191

8.2.1 Covariant Part of the Calculation 193

8.2.2 Discussion and the Nature of the Φ-Representation 196

8.2.3 Concluding Non-Covariant Part of the Calculation 198

8.2.4 Accuracy of the Lamb Shift Calculation 202

Notes 205

Appendix A 213

Appendix B 229

Appendix C 233

References 279

Index 283