Foundations of Classical and Quantum Electrodynamics

Igor N.Toptygin is Professor at the Theoretical Physics Department in Saint-Petersburg State Polytechnic University, Russia. He received his academic degrees in the field of physics and mathematics in 1964 (PhD) and 1974 (habilitation). He is an expert in theoretical physics and theoretical astrophysics. He is a member of the Scientific Council on Complex Problem of "Cosmic Rays" of the Russian Academy of Sciences, and a corresponding member of the International Academy of Sciences for High Education. He has been engaged for many years in theoretical studies of quantum paramagnetic amplifiers, acceleration of cosmic rays, radiation of relativistic particles in plasmas, etc.

• Preface XIFundamental Constants and Frequently Used Numbers XVBasic Notation XVII1 The Mathematical Methods of Electrodynamics 11.1 Vector and Tensor Algebra 11.2 Vector and Tensor Calculus 181.3 The Special Functions of Mathematical Physics 411.4 Answers and Solutions 712 Basic Concepts of Electrodynamics: The Maxwell Equations 912.1 Electrostatics 912.2 Magnetostatics 1122.3 Maxwell's Equations. Free Electromagnetic Field 1312.4 Answers and Solutions 1543 The Special Theory of Relativity and Relativistic Kinematics 1933.1 The Principle of Relativity and Lorentz Transformations 1933.2 Kinematics of Relativistic Particles 2143.3 Answers and Solutions 2334 Fundamentals of Relativistic Mechanics and Field Theory 2714.1 Four-Dimensional Vectors and Tensors 2714.2 The Motion of Charged Particles in Electromagnetic Fields. Transformation of the Electric Field 2804.3 The Four-Dimensional Formulation of Electrodynamics. Introduction to Field Theory 3134.4 Answers and Solutions 3325 Emission and Scattering of Electromagnetic Waves 3955.1 Green's Functions and Retarded Potentials 3955.2 Emission in Nonrelativistic Systems of Charges and Currents 4045.3 Emission by Relativistic Particles 4165.4 Interaction of Charged Particles with Radiation 4365.5 Answers and Solutions 4496 Quantum Theory of Radiation Processes. Photon Emission and Scattering 5136.1 Quantum Theory of the Free Electromagnetic Field 5136.2 Quantum Theory of Photon Emission, Absorption, and Scattering by Atomic Systems 5396.3 Interaction between Relativistic Particles 5606.4 Answers and Solutions 5817 Fundamentals of Quantum Theory of the Electron-Positron Field 6317.1 Covariant Form of the Dirac Equation. Relativistic Bispinor Transformation 6317.2 Covariant Quadratic Forms 6367.3 Charge Conjugation and Wave Functions of Antiparticles 6397.4 Secondary Quantization of the Dirac Field. Creation and Annihilation Operators for Field Quanta 6407.5 Energy and Current Density Operators for Dirac Particles 6437.6 Interaction between Electron-Positron and Electromagnetic Fields 6457.7 Schrödinger Equation for Interacting Fields and the Evolution Operator 6477.8 Scattering Matrix and Its Calculation 6497.9 Calculations of Probabilities and Effective Differential Cross-Sections 6527.10 Scattering of a Relativistic Particle with a Spin in the Coulomb Field 6537.11 Green's Functions of Electron-Positron and Electromagnetic Fields 6577.12 Interaction between Electrons and Muons 6627.13 Higher-Order Corrections 6677.14 Answers and Solutions 669Appendix A Conversion of Electric and Magnetic Quantities between the International System of Units and the Gaussian System 675Appendix B Variation Principle for Continuous Systems 677B.1 Vibrations of an Elastic Medium as the Vibration Limit of Discrete Point Masses 677B.2 The Lagrangian Form of Equations of Motion for a Continuous Medium 680Appendix C General Outline of Quantum Theory 685C.1 Spectrum of Physical Values and the Wave Function 685C.2 State Vector 686C.3 Indistinguishability of Identical Particles 687C.4 Operators and Their Properties 688C.5 Some Useful Formulas of Operator Algebra 698C.6 Wave Functions of the Hydrogen-Like Atom (the Lowest Levels) 699C.6.1 Addition of Angular Moments 700C.6.2 Spin Operators and Wave Functions of Fermions (s D 1/2) 700References 703Index 709