The Electrodynamic Vacuum Field Theory Approach and the Electron Inertia Problem Revisited

It is a review of some new electrodynamics models of interacting charged point particles and related with them fundamental physical aspects, motivated by the classical A. M. Amper's magnetic and H. Lorentz force laws, as well as O. Jefimenko electromagnetic field expressions. Based on the suitably devised vacuum field theory approach the Lagrangian and Hamiltonian reformulations of some alternative classical electrodynamics models are analyzed in detail. A problem closely related to the radiation reaction force is analyzed aiming to explain the Wheeler and Feynman reaction radiation mechanism, well known as the absorption radiation theory, and strongly dependent on the Mach type interaction of a charged point particle in an ambient vacuum electromagnetic medium. There are discussed some relationships between this problem and the one derived within the context of the vacuum field theory approach. The R. Feynman's "heretical" approach to deriving the Lorentz force based Maxwell electromagnetic equations is also revisited, its complete legacy is argued both by means of the geometric considerations and its deep relation with the devised vacuum field theory approach. Based on completely standard reasonings, we reanalyze the Feynman's derivation from the classical Lagrangian and Hamiltonian points of view and construct its nontrivial relativistic generalization compatible with the vacuum field theory approach. The electron inertia problem is reanalyzed within the Lagrangian-Hamiltonian formalisms and the related Feynman proper time paradigm. The validity of the Abraham-Lorentz electromagnetic electron mass origin hypothesis within the shell charged model is argued. The electron stability in the framework of the electromagnetic tension-energy compensation principle is analyzed.