Foundations of Classical and Quantum Electrodynamics

Foundations of Classical and Quantum Electrodynamics

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Bibliographic Details
Main Author: Toptygin, Igor N.
Format: eBook
Language:English
Published: Newark : John Wiley & Sons, Incorporated, 2014.
Series:New York Academy of Sciences Ser.
Subjects:
Quantum electrodynamics > Problems, exercises, etc.
Quantum electrodynamics.
Electronic books.
Online Access:Click for online access
Table of Contents:
  • 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

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