Foundations of Classical Electrodynamics: Charge, Flux, and Metric

Preface * Introduction * Part A--Mathematics: Some Exterior Calculus * Why Exterior Differential Forms? * A.1. Algebra * A.2. Exterior Calculus * A.3. Integration on a Manifold * Part B--Axioms of Classical Electrodynamics * B.1. Electric Charge Conservation * B.2. Lorentz Force Density * B.3. Magnetic Flux Conservation * B.4. Basic Classical Electrodynamics Summarized, Example * B.5. Electromagnetic Energy-Momentum Current and Action* Part C--More Mathematics * C.1. Linear Connection * C.2. Metric * Part D--The Maxwell--Lorentz Spacetime Relation * D.1. A Linear Relation Between H and F * D.2. Propagation of Electromagnetic Waves: Quartic Wave Surface * D.3. First Constraint: Electric/Magnetic Reciprocity * D.4. Second Constraint: Vanishing Skewon Field and Light Cone * D.5. Extracting the Metric by an Alternative Method * D.6. Fifth Axiom: Maxwell--Lorentz Spacetime Relation * Part E--Electrodynamic in Vacuum and in Matter * E.1. Standard Maxwell--Lorentz Theory in a Vacuum * E.2. Electrodynamic Spacetime Relations Beyond Locality and Linearity * E.3. Electrodynamics in Matter, Constitutive Law * Electrodynamics of Moving Continua * Outlook * References * Author Index * Subject Index