Formal Structure of Electromagnetics: General Covariance and Electromagnetics
High-level, explicit treatment of the principle of general covariance as applied to electromagnetics examines the natural invariance of the Maxwell equations, general properties of the medium, nonuniformity, anisotropy and general coordinates in three-space, reciprocity and nonreciprocity, and matter-free space with a gravitational field. 1962 edition.
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TRANSFORMATION BEHAVIOR AND DIMENSIONAL PROPERTIES
NATURAL INVARIANCE OF THE MAXWELL EQUATIONS
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anholonomic arbitrary associated assume Cartesian frames chapter coefficients components consider constant constitutive equations constitutive tensor contravariant covariant derivative covariant vector curl curvilinear coordinates customary d'Alembertian denoted density of weight dielectric differential dimensional dimensions discussed displacement elements energy momentum tensor equations 3.11 expression Faraday effect field equations formation four-dimensional four-potential frame of reference free space Fresnel-Fizeau effect functions fundamental tensor gauge factor geometry Hence identity integral interaction inverse isotropic Jacobian Lagrangian density leads Lie derivative Lorentz transformations magnetic field mathematical matrix matter-free space Maxwell equations medium metric tensor Minkowski natural invariance natural optical activity nonconducting noninstantaneous nonreciprocal nonuniform obtained optical activity permeability permittivity permutation field phase velocity physical fields potential principle propagation properties pseudo tensor reciprocal relation represents restricted Riemann tensor rotation scalar SCHOUTEN space-time manifold spatial structural field symmetry tensor density theory tion trans transformation behavior uniform valence vanish variational vector density wave equation zero