Advanced quantum mechanics / Freeman Dyson ; translated and transcribed by David Derbes.

Includes bibliographical references and index.

Foreword; Notes; Preface; Preface to First Edition; Contents; 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 Approximation2.13 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 Theory4.2 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 Operators5.1.4 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 Renormalization5.3 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

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 19.

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