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Topological Foundations of Electromagnetism seeks a fundamental understanding of the dynamics of electromagnetism; and marshals the evidence that in certain precisely defined topological conditions, electromagnetic theory (Maxwell's theory) must be extended or generalized in order to provide an explanation and understanding of, until now, unusual electromagnetic phenomena. Key to this generalization is an understanding of the circumstances under which the so-called A potential fields have physical effects. Basic to the approach taken is that the topological composition of electr

Electromagnetism. --- Magnetism. --- Mathematical physics --- Physics --- Electricity --- Magnetics --- Electromagnetics --- Magnetic induction --- Magnetism --- Metamaterials

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Divergencies in quantum field theory referred to as "infinite zero-point energy" have been a problem for 70 years. Renormalization has always been considered an unsatisfactory remedy. In 1985 it was found that Maxwell's equations generally do not have solutions that satisfy the causality law. An additional term for magnetic dipole currents corrected this shortcoming. Rotating magnetic dipoles produce magnetic dipole currents, just as rotating electric dipoles in a material like barium titanate produce electric dipole currents. Electric dipole currents were always part of Maxwell's equations.

Maxwell equations. --- Quantum electrodynamics. --- Electrodynamics, Quantum --- QED (Physics) --- Quantum field theory --- Schwinger action principle --- Equations, Maxwell --- Differential equations, Partial --- Electromagnetic theory