. We find that the exact equation of motion does not exhibit runaway solutions or non-causal behavior, when the cut-off is larger than half of the classical radius of the electron. The calculation of the self-force acting on a charged particle is a long outstanding problem in electrodynamics since

A simple mathematical procedure is introduced which allows redefining in a precise way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once removed without affecting the locality

-energy continuum of the Dirac equation. The resulting possibility of spontaneous positron production and the new concept of a charged electron-positron vacuum is discussed under several aspects. The autoionization model and the exact overcritical solutions of the single-particle Dirac equation are contrasted

In the framework of classical electrodynamics elementary particles are treated as capacitors. The electrostatic potentials satisfy equations of the Schrödinger type. An interesting “quantization condition ” for elementary charges is derived.

In the present work a number of questions concerning foundations of the classical electrodynamics are discussed. First of all these are the law of conservation of energy and the introduction of particles in classical electrodynamics. We pay attention to a logical error which appears

In the present work a number of questions concerning foundations of the classical electrodynamics is discussed. First of all they are the law of the energy conservation and the introduction of particles in the classical electrodynamics. We pay attention to a logic error which takes place

of “gauge renormalization”, which allows transforming the divergent terms of classical electrodynamics (infinite self-force, self-energy and self-momentum) to converging integrals. The motional equation obtained for a non-radiating charged particle does not contain its self-force, and the mass parameter

A system consisting of an equilibrium medium formed by charged parti-cles and electromagnetic field is considered in the classical case at weak interaction between subsystems. The field is described with all the statis-tical moments of electric and magnetic fields. The moments are reduced

There are known problems with the standard Lorentz-Dirac description of radiation reaction in classical electrodynamics. The model of extended in one dimension particle is proposed and is shown that for this model there is no total change in particle momentum due to radiation reaction. 03.50.De

Given the conventional Maxwell–Lorentz formulation of classical electrodynamics in a flat spacetime of arbitrary odd dimension, the retarded vector potential A µ generated by a point-like charge is found to be pure gauge, A µ = ∂ µ χ. By the Gauss law, the charge vanishes. Therefore, classical