Contents -- Foreword -- Notes -- Preface -- Preface to First Edition -- Generally used Notation -- 1 Introduction -- 1.1 Books -- 1.2 Subject Matter -- 1.3 Detailed Program -- 1.4 One-Particle Theories -- 2 The Dirac Theory -- 2.1 The Form of the Dirac Equation -- 2.2 Lorentz Invariance of the Dirac Equation -- 2.3 To Find the S -- 2.4 The Covariant Notation -- 2.5 Conservation Laws. Existence of Spin -- 2.6 Elementary Solutions -- 2.7 The Hole Theory -- 2.8 Positron States -- 2.9 Electromagnetic Properties of the Electron -- 2.10 The Hydrogen Atom -- 2.11 Solution of Radial Equation -- 2.12 Behaviour of an Electron in a Non-Relativistic Approximation -- 2.13 Summary of Matrices in the Dirac Theory in Our Notation -- 2.14 Summary of Matrices in the Dirac Theory in the Feynman Notation -- 3 Scattering Problems and Born Approximation -- 3.1 General Discussion -- 3.2 Projection Operators -- 3.3 Calculation of Traces -- 3.4 Scattering of Two Electrons in Born Approximation. The Møller Formula -- 3.5 Relation of Cross-sections to Transition Amplitudes -- 3.6 Results for Møller Scattering -- 3.7 Note on the Treatment of Exchange Effects -- 3.8 Relativistic Treatment of Several Particles -- 4 Field Theory -- 4.1 Classical Relativistic Field Theory -- 4.2 Quantum Relativistic Field Theory -- 4.3 The Feynman Method of Quantization -- 4.4 The Schwinger Action Principle -- 4.4.1 The Field Equations -- 4.4.2 The Schrodinger Equation for the State-function -- 4.4.3 Operator Form of the Schwinger Principle -- 4.4.4 The Canonical Commutation Laws -- 4.4.5 The Heisenberg Equation of Motion for the Operators -- 4.4.6 General Covariant Commutation Laws -- 4.4.7 Anticommuting Fields -- 5 Examples of Quantized Field Theories -- 5.1 The Maxwell Field -- 5.1.1 Momentum Representations -- 5.1.2 Fourier Analysis of Operators -- 5.1.3 Emission and Absorption Operators.

5.1.4 Gauge-Invariance of the Theory -- 5.1.5 The Vacuum State -- 5.1.6 The Gupta-Bleuler Method -- 5.1.7 Example: Spontaneous Emission of Radiation -- 5.1.8 The Hamiltonian Operator -- 5.1.9 Fluctuations of the Fields -- 5.1.10 Fluctuation of Position of an Electron in a Quantized Electromagnetic Field. The Lamb Shift -- 5.2 Theory of Line Shift and Line Width -- 5.2.1 The Interaction Representation -- 5.2.2 The Application of the Interaction Representation to the Theory of Line-Shift and Line-Width -- 5.2.3 Calculation of Line-Shift, Non-Relativistic Theory -- 5.2.4 The Idea of Mass Renormalization -- 5.3 Field Theory of the Dirac Electron, Without Interaction -- 5.3.1 Covariant Commutation Rules -- 5.3.2 Momentum Representations -- 5.3.3 Fourier Analysis of Operators -- 5.3.4 Emission and Absorption Operators -- 5.3.5 Charge-Symmetrical Representation -- 5.3.6 The Hamiltonian -- 5.3.7 Failure of Theory with Commuting Fields -- 5.3.8 The Exclusion Principle -- 5.3.9 The Vacuum State -- 5.4 Field Theory of Dirac Electron in External Field -- 5.4.1 Covariant Commutation Rules -- 5.4.2 The Hamiltonian -- 5.4.3 Antisymmetry of the States -- 5.4.4 Polarization of the Vacuum -- 5.4.5 Calculation of Momentum Integrals -- 5.4.6 Physical Meaning of the Vacuum Polarization -- 5.4.7 Vacuum Polarization for Slowly Varying Weak Fields. The Uehling Effect -- 5.5 Field Theory of Dirac and Maxwell Fields in Interaction -- 5.5.1 The Complete Relativistic Quantum Electrodynamics -- 5.5.2 Free Interaction Representation -- 6 Free Particle Scattering Problems -- 6.1 Møller Scattering of Two Electrons -- 6.1.1 Properties of the DF Function -- 6.1.2 The Møller Formula, Conclusion -- 6.1.3 Electron-Positron Scattering -- 6.2 Scattering of a Photon by an Electron. The Compton Effect. Klein-Nishina Formula -- 6.2.1 Calculation of the Cross-Section -- 6.2.2 Sum Over Spins.

6.3 Two Quantum Pair Annihilation -- 6.4 Bremsstrahlung and Pair Creation in the Coulomb Field of an Atom -- 7 General Theory of Free Particle Scattering -- 7.1 The Reduction of an Operator to Normal Form -- 7.2 Feynman Graphs -- 7.3 Feynman Rules of Calculation -- 7.4 The Self-Energy of the Electron -- 7.5 Second-Order Radiative Corrections to Scattering -- 7.6 The Treatment of Low-Frequency Photons. The Infra-Red Catastrophe -- 8 Scattering by a Static Potential. Comparison with Experimental Results -- 8.1 The Magnetic Moment of the Electron -- 8.2 Relativistic Calculation of the Lamb Shift -- 8.2.1 Covariant Part of the Calculation -- 8.2.2 Discussion and the Nature of the -Representation -- 8.2.3 Concluding Non-Covariant Part of the Calculation -- 8.2.4 Accuracy of the Lamb Shift Calculation -- Notes -- Appendices -- Appendix A -- A.1 Particle Mechanics and Field Mechanics -- A.2 Classical Particle Mechanics -- A.3 Classical Relativistic Field Theory -- A.4 Particle Quantum Mechanics -- A.5 Huyghens' Principle and the Feynman Method of Quantization -- A.6 The Feynman Quantization for Field Theory -- A.7 The Schwinger Action Principle for Particle Mechanics -- A.8 Equivalence of the Schwinger Action Principle with Ordinary Quantum Mechanics -- A.8.1. The Operator Equations of Motion -- A.8.2. The Commutation Rules -- A.8.3. The Schrodinger Equation -- A.9 Transition to Field Theory -- Appendix B -- Appendix C -- C.1 The Interaction Representation -- C.2 Contribution of the Interaction (9, 2) -- C.3 Calculation of the Term (1, 6) -- C.4 Gauge Invariance in the Theory -- C.5 Consequences of the Invariance -- C.6 Possibility of Renormalization to All Orders -- C.7 Types of Divergence -- C.8 The Self-Energy of the Vacuum: Diagrams of the Form etc. (G1) -- C.9 Furry's Theorem2 -- C.10 (A) Self-Energy of the Photon.

C.11 (B) Scattering of Light by Light -- C.12 (C) The Vertex Part -- C.13 (D) Self-Energy of the Electron -- C.14 (D) Last Tasks -- C.14.1 First Case -- C.14.2 Second Case -- C.14.3 Calculation of the Renormalized Diagrams of Order Ae(A)4 -- Notes -- References -- Index.