The Classical Electrodynamic Part of Landau and Lifshitz's Textbook The Classical Theory of Fields is rigorously analyzed. The need for corrections is proved. The distinction between bound fields and radiation fields is stipulated. Apparent paradoxes, like the "hidden momentum" concept and the 4/3 factor of the Lorentz transformation of the electromagnetic fields' momentum of a charged particle are explained. Inherent contradictions of of the gauge transformations are proved. In particular, it is proved that the apparent gauge invariance of the QED Lagrangian density does not hold because of its inherent mathematical inconsistencies. This analysis clarifies the long debate concerning the meaning of the electromagnetic 4-potential and its gauge transformations. A regular magnetic monopole theory is outlined, and the systematic failure of the quest for Dirac monopoles is proved.
Eliahu Comay demonstrated his research abilities in the field of electrodynamics when he was the first person [1,2] who proved that the hidden momentum is actually an explicit mechanical momentum that is associated with the system’s mechanical energy-momentum tensor of the magnet’s electric current.
References:
[1] R. H. Romer, Am. J. Phys., 63, 777 (1995).
[2] E. Comay, Exposing “Hidden Momentum”, Am. J. Phys., 64, 1028 (1996)