Quantum Electrodynamics

The following sections are included:

• FOREWORD

• CONTENTS

The following sections are included:

• Introduction

• Survey of Tests of QED

• Condensed-matter Physics Determination of α

• Acknowledgements

• References

The following sections are included:

• Present Status of Construction of Field Models

• Construction of the System and Main Results

• Outline of the Proof

• Several Properties of the Resultant Theory

• What We Can Learn from the Model

• References

The following sections are included:

• INTRODUCTION

• DIFFICULTY OF THE AXIAL-TYPE GAUGES

• INDEFINITE METRIC AND SUBSIDIARY CONDITION

• DIPOLE GHOSTS AND THE B-FIELD FORMALISM

• GOTO-IMAMURA DIFFICULTY AND THE SCHWINGER TERM

• INFRARED PROBLEM

• ELECTRON'S ASYMPTOTIC FIELD AND THE GAUSS LAW

• FINITENESS OF THE RENORMALIZATION CONSTANTS

• REFERENCES

The following sections are included:

• Introduction

• The Cut-off in QED

• Nonrelativistic Quantum Electrodynamics (NRQED)

• NRQED for Positronium and Other Simple Atoms

• NRQED for Condensed-Matter Systems

• Acknowledgements

• References

The following sections are included:

• Introduction

• Interaction Lagrangians and couplings
  • The electromagnetic interaction
  • The electroweak interaction

• Cross sections in lowest order
  • e⁺e⁻ → γγ
  • 
  • e⁺e⁻ → γγ e⁺e⁻

• Radiative corrections
  • e⁺e⁻ → γγ, γγγ
  • 
  • e⁺e⁻ → γγ e⁺e⁻, e⁺e⁻γ
  • Event generators

• Photon–photon collision cross sections

• Experiments

• Experimental tests of QED
  • Two particle final states
    • e⁺e⁻ → γγ
    • e⁺e⁻ → e⁺e⁻
    • e⁺e⁻ → μ⁺μ⁻ and e⁺e⁻ → τ⁺τ⁻
  • Hard photon radiation processes
  • Photon–photon collisions

• Experimental tests of QFD
  • Lepton asymmetries
  • Quark asymmetries
  • Total hadronic cross section
  • Beyond the standard theory

• Conclusion

• References

The following sections are included:

• INTRODUCTION

• GENERAL FORMALISM
  • Magnetic Moment Projection Operators
  • Second Order Example
  • Extraction of Divergences
    • Extraction of Ultraviolet Divergences
    • Extraction of Infrared Divergences

• HYPERSPHERICAL FORMALISM
  • Performing the Angular Integrals
  • Performing the “Radial” Integrations, General Approach
  • Second Order Example
  • Details of the Radial Integrals

• DISPERSION RELATIONS FORMALISM
  • Second Order Example
  • Form Factors
  • Applications of dispersion relations to graphs with vacuum polarization

• HYBRID DISPERSIVE AND HYPERSPHERICAL APPROACH

• APPENDIX
  • Divergences in the Hyperspherical Formalism
    • Removal of Infrared Divergences
  • Difficult Angular Integrals
  • Dispersion relation for vector and tensor quantities
  • Infrared Divergences in the Dispersive Formalism
  • Polylogarithms
  • Analytic Results

• References

The following sections are included:

• Introduction and Summary

• A Parametric Formulation of Perturbation Theory for QED
  • Introductory remarks
  • Feynman-Dyson rules for parametric integrals
  • Amplitudes for proper self-energy and vertex diagrams
  • Magnetic moment from a set of proper vertices summed by the Ward-Takahashi identity

• Divergence Structure of Renormalization Constants
  • K_s and I_R operations
  • Second-order renormalization constants
  • Second-order graphs with mass insertion
  • Fourth-order renormalization constants
  • Sixth-order renormalization constants

• Electron Anomalous Moment without Closed Electron Loops
  • Second-order term
  • Fourth-order terms
  • Fourth-order terms with mass insertion
  • Sixth-order terms
  • Eighth-order terms

• Electron Anomalous Moment with Closed Electron Loops
  • Feynman-parametric form of the photon spectral function
  • Fourth-order term
  • Sixth-order terms
  • Eighth-order terms

• Comments on the Numerical Integration
  • Introductory remarks
  • Adaptive Monte-Carlo integration routine VEGAS
  • Problems encountered in high-precision numerical integration

• Acknowledgments

• Appendix A. B_αβ for Four-loop Chain Diagrams

• Appendix B. Divergence Structure of the Sixth-order Renormalization Constants

• Appendix C. Renormalization Scheme for Sixth-order Moments of the Three-photon Exchange Type

• Appendix D. Intermediate Renormalization of Eighth-order Moments of the Four-photon Exchange Type

• References

The following sections are included:

• Introduction
  • Historical Overview
  • Basic Description

• Apparatus
  • Various Traps
  • Compensation Feature
  • Adaptations for Positrons

• Axial Resonance
  • Stable Ring-Endcap Potential
  • Detection of Trapped Charge
  • Isolating the Single Electron
  • Magnetic Coupling
  • Other Axial Shifts

• Magnetron Motion
  • The “Resonance”
  • Changing the Magnetron Orbit
  • Frequency Shifts

• Cyclotron Resonance
  • Microwave System
  • Lineshape
  • Perturbations to the Cyclotron Frequency
  • Cavity Effects
  • Observed Shift vs Cyclotron Drive

• Anomaly Resonance
  • The Clean “Beat-Note“
  • Axial Excitation Technique
  • Guard-Ring Excitation Technique
  • The Resonance Lineshape

• Results, Conclusions, and Goals
  • The g-Factor Results
  • “a_e” and QED
  • Potential Future Efforts

• References

The following sections are included:

• Introduction and History

• One-electron Cyclotron Oscillator

• Simple Model

• Cylindrical, Hyperbolic and Spherical Cavities

• Implication for current experiments

• Renormalized calculation of cavity shifts
  • Renormalization
  • Spherical cavity
  • Cylindrical cavity

• Summary and future prospects

• References

The following sections are included:

• Introduction and Summary

• QED Contribution to the Muon Anomaly
  • Preliminary remarks
  • Fourth-order terms
  • Sixth-order terms
  • Eighth-order terms
    • Group I diagrams
    • Group II diagrams
    • Group III diagrams
    • Group IV diagrams
    • Other eighth-order terms
  • Tenth-order terms – a preliminary estimate

• Application of the Renormalization Group Method to α_μ

• Hadronic Contributions to the Muon Anomaly
  • Introductory remarks
  • Hadronic vacuum-polarization contribution to α_μ
  • Hadronic light-by-light scattering contribution to α_μ
    • Charged-pion-loop contribution
    • Incorporating the vector-meson-dominance picture
    • Resonance contributions

• Weak Contributions to α_μ

• “New Physics” Contributions
  • Extra Gauge Bosons
  • Additional Higgs Scalars
  • Supersymmetry
  • Compositeness
  • Electric dipole moments
  • Concluding remarks

• Acknowledgments

• References

The following sections are included:

• INTRODUCTION

• SURVEY OF THE THEORY

• MUON PRECESSION AT REST

• MUON PRECESSION IN FLIGHT
  • Magnetic Field Only
  • Magnetic and Electric Field
  • Pitch Correction
  • Experimental Principles

• INITIAL MUON POLARIZATION AND MEASUREMENT OF THE FINAL POLARIZATION
  • Generalities
  • From an Ideal (g - 2) Experiment to a Real One

• 1958–1962: THE (g – 2) EXPERIMENT AT THE CERN SYNCHRO-CYGLOTRON

• 1962–1968: MUON STORAGE RING I
  • A General View
  • The Injection System For Muon Storage Rings
  • Some General Considerations for Calculating the Number of Muons Stored in a Storage Ring
  • The Count Rate N(t) versus f_a

• 1969–1976: MUON STORAGE RING II
  • The Second (g – 2) Experiment at the Proton Synchrotron
  • Electric Field and Vacuum
  • Electric Scraping
  • The Storage Ring Magnet
  • Stabilization and Reproducibility of the Magnetic Field
  • Radial Distribution of Muons and Magnetic Field Analysis
  • Data Analysis
  • Experimental Results
  • Comparison Between Theory and Experiment
  • Comparison between the Muon and Electron g-Factor Experiments

• ELECTRIC DIPOLE MOMENT

• MUON LIFETIME IN FLIGHT

• VERIFICATION OF THE CPT THEOREM

• THE SITUATION TOMORROW: PLANS FOR A NEW MEASUREMENT
  • A Fourth (g – 2) Experiment
  • The Muon Distribution and the Average Field
  • Pick-Up Electrodes
  • Magnet
  • Electronics
  • Inflector
  • Summary

• FINAL REMARKS

• Acknowledgements

• REFERENCES

The following sections are included:

• INTRODUCTION

• PRESENT STATUS OF THEORY AND COMPARISON WITH EXPERIMENT

• THEORETICAL METHODS IN THE NON-RECOIL LIMIT

• FORMULATION QF AN EQUATION FOR BOUND STATE QED CALCULATIONS

• PURE RECOIL CORRECTIONS

• RADIATIVE-RECOIL CORRECTIONS

• Acknowledgements

• APPENDICES

• REFERENCES

The following sections are included:

• Early History

• Atomic Beam Deflection Experiments

• Atomic Beam Refocussing Experiments

• Atomic Beam Magnetic Resonance Experiments

• Anomalous Magnetic Moment of the Electron

• Atomic Hydrogen Maser Experiments

• Dependence of Hyperfine Structure on External Magnetic Field

• Dependence of Hyperfine Structure on External Electric Field

• Hyperfine Structure Experiments in Higher Electronic States

• Further Theoretical Discussion

• REFERENCES

The following sections are included:

• INTRODUCTION

• SUMMARY OF THEORY

• CALCULATION OF SIGNALS

• SLOW BEAM MEASUREMENTS

• BOTTLE EXPERIMENTS

• FAST BEAM EXPERIMENTS
  • Stark Quenching
  • Anisotropy of Quench Radiation
  • Quantum Beat Experiments
  • Atomic Interferometer
  • Fast Beam Radiofrequency Experiments
    • Single Field
    • Separated Oscillatory Fields
  • Fast Beam Laser Resonance

• LASER SPECTROSCOPY

• DIRECT MEASUREMENT OF LYMAN-a RADIATION

• EXOTIC ATOMS

• TWO ELECTRON ATOMS

• COMPARISON OF THEORY AND EXPERIMENT
  • Hydrogne
  • Helium
  • High Z Atoms

• PROSPECTS

• ACKNOWLEDGEMENTS

• References

The following sections are included:

• INTRODUCTION

• METHODS OF POSITRONIUM FORMATION
  • Ps in Gases and Powders
  • Ps in Vacuum

• MEASUREMENTS OF THE PHYSICAL PROPERTIES
  • Positronium Mass
  • Annihilation Rates
  • Positronium Energy Levels
    • Hyperfine Interval
    • Positronium n=2 Fine Structure
    • 1S-2S Interval
    • Rydberg Levels
  • Positronium Negative Ion

• EXOTICA
  • Tests of Discrete Symmetries
  • Exotic Decays
  • Cryogenic Positronium

• ACKNOWLEDGMENTS

• REFERENCES

The following sections are included:

• INTRODUCTION

• THEORY OF MUONIUM ENERGY LEVELS
  • Schroedinger Equation
  • Brett Equation
  • Hyperfine Structure Interval in Ground State
  • Zeeman Effect in 1²S_1/2 Ground State
  • Fine Structure and Lamb Shift in n = 2 Excited State
  • Muonium Decay

• DISCOVERY OF MUONIUM AND MUONIUM FORMATION
  • Theoretical Considerations on Muonium Formation
  • Discovery of Muonium and Other Muonium Formation Experiments

• HYPERFINE STRUCTURE AND ZEEMAN EFFECT IN GROUND STATE MUONIUM
  • Transition Frequencies
  • Theory of Resonance Line Shape
  • Measurements at Strong Magnetic Field
  • Measurements at Weak Magnetic Field
  • Summary and Prospectlves

• THE LAMB SHIFT IN MUONIUM
  • Introduction
  • Muonium Production in Vacuum by the Beam Foil Method
  • Observation of Muonlum in the 2S State by Static Electric Field Quenching
  • Observation and Measurement of the Lamb Shift Transition

• THE 1S–2S TRANSITION IN MUONIUM

• MUONIC HELIUM ATOM

• REFERENCES

The following sections are included:

• INTRODUCTION

• EXPERIMENT
  • The first optical and microwave experiments
  • Level crossing measurements
  • Atomic Beam Measurements
    • General description of the experiments
    • Optical excitation
    • Microwave systems
    • Detector systems
    • Magnetic field measurement
    • Atomic beam

• THEORY
  • Wave-functions
  • Quantum Electrodynamic Contributions
  • Higher Order Contributions

• RESULTS

• OUTLOOK FOR THE FUTURE
  • Improvement in Beam Intensity
  • Selective Excitation of the 2³P State
  • Projected errors

• OTHER FINE-STRUCTURE INTERVALS OF HELIUM AND TWO-ELECTRON IONS

• ACKNOWLEDGEMENTS

• References

The following sections are included:

• APPENDIX: HISTORICAL REVIEW AND BIBLIOGRAPHY OF QUANTUM ELECTRODYNAMICS

• BIBLIOGRAPHY