Foundations of classical and quantum electrodynamics / / Igor N. Toptygin

• Autore: Toptygin I. N (Igor Nikolaevich)
• Pubblicazione: Somerset County, New Jersey : , : Wiley-VCH, , [2013]; 2014
• Descrizione fisica: 1 online resource (734 p.)
• Disciplina: 530.1433
• Soggetto topico: Quantum electrodynamics
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover -- Title Page -- Contents -- Preface -- Fundamental Constants and Frequently Used Numbers -- Basic Notation -- 1 The Mathematical Methods of Electrodynamics -- 1.1 Vector and Tensor Algebra -- 1.1.1 The Definition of a Tensor and Tensor Operations -- 1.1.2 The Principal Values and Invariants of a Symmetric Tensor of Rank 2 -- 1.1.3 Covariant and Contravariant Components -- 1.1.4 Tensors in Curvilinear and Nonorthogonal Systems of Coordinates -- 1.2 Vector and Tensor Calculus -- 1.2.1 Gradient and Directional Derivative. Vector Lines -- 1.2.2 Divergence and Curl. Integral Theorems -- 1.2.3 Solenoidal and Potential (Curl-less) Vectors -- 1.2.4 Differential Operations of Second Order -- 1.2.5 Differentiating in Curvilinear Coordinates -- 1.2.6 Orthogonal Curvilinear Coordinates -- 1.3 The Special Functions of Mathematical Physics -- 1.3.1 Cylindrical Functions -- 1.3.2 Spherical Functions and Legendre Polynomials -- 1.3.3 Dirac Delta Function -- 1.3.4 Certain Representations of the Delta Function -- 1.3.5 The Representation of the Delta Function through Loop Integrals in a Complex Plane -- 1.3.6 Expansion in Total Systems of Orthogonal and Normalized Functions. General Considerations -- 1.3.7 Fourier Series -- 1.3.8 Fourier Integral -- 1.4 Answers and Solutions -- 2 Basic Concepts of Electrodynamics: The Maxwell Equations -- 2.1 Electrostatics -- 2.1.1 The Coulomb Law -- 2.1.2 Electric Field -- 2.1.3 Energy and Forces in Electrostatic Fields -- 2.2 Magnetostatics -- 2.2.1 Current Density and the Magnetic Field. Biot-Savart Law -- 2.2.2 Lorentz Force and Ampère's Formula -- 2.2.3 Conservation of Electric Charge and the Continuity Equation -- 2.2.4 Equations of Magnetostatics. Vector Potential -- 2.2.5 Energy and Forces in Magnetostatic Fields -- 2.3 Maxwell's Equations. Free Electromagnetic Field -- 2.3.1 The Law of Electromagnetic Induction. ; 2.3.2 The Systems of Measurement Units of Electric and Magnetic Values -- 2.3.3 An Analysis of the System of Maxwell's Equations -- 2.3.4 Free Electromagnetic Field -- 2.3.5 The Partial Polarization of Waves -- 2.3.6 Analytical Signal -- 2.3.7 The Hamiltonian Form of Equations for a Free Electromagnetic Field -- 2.4 Answers and Solutions -- 3 The Special Theory of Relativity and Relativistic Kinematics -- 3.1 The Principle of Relativity and Lorentz Transformations -- 3.1.1 Properties of Space-Time and Intervals -- 3.1.2 Lorentz Transformations -- 3.1.3 Pseudo-Euclidean Geometry -- 3.2 Kinematics of Relativistic Particles -- 3.2.1 Energy and Momentum -- 3.2.2 Kinematic Problems -- 3.3 Answers and Solutions -- 4 Fundamentals of Relativistic Mechanics and Field Theory -- 4.1 Four-Dimensional Vectors and Tensors -- 4.1.1 Transformations of Tensors -- 4.1.2 Dual Tensors -- 4.2 The Motion of Charged Particles in Electromagnetic Fields. Transformation of the Electric Field -- 4.2.1 Interaction of Charged Particles with the Electromagnetic Field -- 4.2.2 Equations of Motion of a Relativistic Particle -- 4.2.3 Transformations of Electromagnetic Field Stress -- 4.2.4 Dynamics of Orbital and Spin Magnetic Moments -- 4.2.5 The Approximate Methods. Averaging over Rapid Movements -- 4.3 The Four-Dimensional Formulation of Electrodynamics. Introduction to Field Theory -- 4.3.1 Lagrangian and Hamiltonian Methods in Field Theory -- 4.3.2 The Action for an Electromagnetic Field -- 4.3.3 Noether's Theorem and Integrals of Motion -- 4.4 Answers and Solutions -- 5 Emission and Scattering of Electromagnetic Waves -- 5.1 Green's Functions and Retarded Potentials -- 5.1.1 The Green's Function of a Wave Equation -- 5.1.2 Retarded Potentials -- 5.1.3 The Spectral Composition of Emission -- 5.2 Emission in Nonrelativistic Systems of Charges and Currents. ; 5.2.1 Electric Dipole Emission -- 5.2.2 Quadrupole and Magnetic Dipole Emission -- 5.2.3 The Hertz Vector and Antenna Radiation -- 5.3 Emission by Relativistic Particles -- 5.3.1 The Electromagnetic Field of a Propagating Charged Particle -- 5.3.2 The Loss of Energy and Momentum of a Charged Particle -- 5.3.3 The Spectral Distribution of Radiation Emitted by Relativistic Particles -- 5.3.4 Radiation from Colliding Particles -- 5.3.5 Radiation from Particle Decays and Transformations -- 5.4 Interaction of Charged Particles with Radiation -- 5.4.1 Interaction of a Charged Particle with its Own Electromagnetic Field -- 5.4.2 Renormalization of Mass. The Radiation Damping Force in the Relativistic Case -- 5.4.3 Scattering of ElectromagneticWaves by Particles -- 5.5 Answers and Solutions -- 6 Quantum Theory of Radiation Processes. Photon Emission and Scattering -- 6.1 Quantum Theory of the Free Electromagnetic Field -- 6.1.1 Field Oscillators -- 6.1.2 Photons -- 6.1.3 Occupation Number Representation and Operators of the Electromagnetic Field -- 6.1.4 Coherent States -- 6.1.5 Representation of the Quantum States and the Operators in the Basis of Coherent States -- 6.1.6 Squeezed States -- 6.1.7 Entangled States -- 6.1.8 Beamsplitters -- 6.2 Quantum Theory of Photon Emission, Absorption, and Scattering by Atomic Systems -- 6.2.1 Interaction of the Quantized Electromagnetic Field with a Nonrelativistic System -- 6.2.2 Spontaneous and Stimulated Emission -- 6.2.3 Electric Dipole Radiation -- 6.2.4 Electric Quadrupole and Magnetic Dipole Radiation -- 6.2.5 Perturbation Theory for the Density Matrix -- 6.2.6 Long-Wavelength Dipole Approximation -- 6.3 Interaction between Relativistic Particles -- 6.3.1 The Relativistic Dirac Equation for Fermions -- 6.3.2 The Klein-Gordon-Fock Equation -- 6.3.3 The Analysis of the Dirac Equation. ; 6.3.4 The Interaction Operator of a Relativistic Particle with Photons -- 6.3.5 Method of Equivalent Photons -- 6.4 Answers and Solutions -- 7 Fundamentals of Quantum Theory of the Electron-Positron Field -- 7.1 Covariant Form of the Dirac Equation. Relativistic Bispinor Transformation -- 7.2 Covariant Quadratic Forms -- 7.3 Charge Conjugation and Wave Functions of Antiparticles -- 7.4 Secondary Quantization of the Dirac Field. Creation and Annihilation Operators for Field Quanta -- 7.5 Energy and Current Density Operators for Dirac Particles -- 7.6 Interaction between Electron-Positron and Electromagnetic Fields -- 7.7 Schrödinger Equation for Interacting Fields and the Evolution Operator -- 7.8 Scattering Matrix and Its Calculation -- 7.9 Calculations of Probabilities and Effective Differential Cross-Sections -- 7.10 Scattering of a Relativistic Particle with a Spin in the Coulomb Field -- 7.11 Green's Functions of Electron-Positron and Electromagnetic Fields -- 7.12 Interaction between Electrons and Muons -- 7.12.1 Electron-Muon Collisions -- 7.12.2 Conversion of an Electron-Positron Pair into a Muon Pair -- 7.13 Higher-Order Corrections -- 7.14 Answers and Solutions -- Appendix A Conversion of Electric and Magnetic Quantities between the International System of Units and the Gaussian System -- Appendix B Variation Principle for Continuous Systems -- B.1 Vibrations of an Elastic Medium as the Vibration Limit of Discrete Point Masses -- B.2 The Lagrangian Form of Equations of Motion for a Continuous Medium -- Appendix C General Outline of Quantum Theory -- C.1 Spectrum of Physical Values and the Wave Function -- C.2 State Vector -- C.3 Indistinguishability of Identical Particles -- C.4 Operators and Their Properties -- C.5 Some Useful Formulas of Operator Algebra -- C.6 Wave Functions of the Hydrogen-Like Atom (the Lowest Levels). ; C.6.1 Addition of Angular Moments -- C.6.2 Spin Operators and Wave Functions of Fermions (s = 1/2) -- References -- Index.
• Sommario/riassunto: This advanced textbook covers many fundamental, traditional and new branches of electrodynamics, as well as the related fields of special relativity, quantum mechanics and quantum electrodynamics. The book introduces the material at different levels, oriented towards 3rd-4th year bachelor, master, and PhD students. This is so as to describe the whole complexity of physical phenomena, instead of a mosaic of disconnected data. The required mathematical background is collated in Chapter 1, while the necessary physical background is included in the main text of the corresponding chapters and a
• Titolo autorizzato: Foundations of classical and quantum electrodynamics
• ISBN: 3-527-67751-8; 3-527-68042-X; 3-527-67749-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910787757003321
• Lo trovi qui: Univ. Federico II
• Serie: New York Academy of Sciences