Foundations of Classical Electrodynamics: Charge, Flux, and Metric (Hardcover, 2003)

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