Modern Classical Electrodynamics and Electromagnetic Radiation - Vacuum Field Theory Aspects

TL;DR

This paper explores new classical electrodynamics models based on vacuum field theory, analyzing radiation reaction forces, revisiting Feynman's approach, and proposing relativistic generalizations within a geometric framework.

Contribution

It introduces alternative classical electrodynamics models using vacuum field theory, reformulates them in Lagrangian and Hamiltonian terms, and extends Feynman's derivation relativistically within this approach.

Findings

Reformulated electrodynamics models using vacuum field theory.

Analyzed radiation reaction and Wheeler-Feynman absorption mechanisms.

Developed relativistic generalizations of Feynman's approach.

Abstract

The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and related with them physical aspects. Based on the vacuum field theory no-geometry approach, developed in \cite{BPT,BPT1}, the Lagrangian and Hamiltonian reformulations of some alternative classical electrodynamics models are devised. 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 \textquotedblleft heretical\textquotedblright\ approach \cite{Dy1,Dy2} 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 vacuum field theory approach devised before in \cite{BPT0,BPT1}. \ Being completely classical, we reanalyze the Feynman's derivation from the classical Lagrangian and Hamiltonian points of view \ and construct its nontrivial \ relativistic generalization compatible with the mentioned above vacuum field theory approach.