Classical electrodynamics with vacuum polarization: electron self-energy and radiation reaction

The classical theory of radiating point-charges is revisited: the retarded potentials, fields, and currents are defined as nonlinear generalized functions and all calculations are made in a Colombeau algebra. The total rate of energy-momentum radiated by an arbitrarily moving relativistic point-charge under the effect of its own field is shown to be rigorously equal to minus the self-interaction force due to that field. This solves, without changing anything in Maxwell's theo...

The theory of point-particles in classical electrodynamics has a well-known problem of infinite self-energy, and the same is true of quantum electrodynamics. Instead of concluding that there is no such thing as a true point-particle, it is shown here how to remove the infinities by supposing that the electromagnetic field tensor has a symmetric part. This does not change the physics, as the equation of motion and the antisymmetric part of the retarded fields appearing in the ...

We present a consistent extended-object approach for determining the self force acting on an accelerating charged particle. In this approach one considers an extended charged object of finite size $\epsilon $, and calculates the overall contribution of the mutual electromagnetic forces. Previous implementations of this approach yielded divergent terms $\propto 1/\epsilon $ that could not be cured by mass-renormalization. Here we explain the origin of this problem and fix it. ...

In this paper we investigate the link between classical electrodynamics and the mass-energy equivalence principle, in view of the conclusions reached in ref.[1]. A formula for the radius of a charged particle is derived. The formula predicts the radius of the proton correctly. The radius of the electron turns out to be a surprising quantity that solves the existing problems of electrodynamics, particularly the problem of the infinite self-force of the electron. In addition, t...

The problems of Classical Electrodynamics with the electron equation of motion and with non-integrable singularity of its self-field stress tensor are well known. They are consequences, we show, of neglecting terms that are null off the charge world line but that gives a non null contribution on its world line. The self-field stress tensor of a point classical electron is integrable, there is no causality violation and no conflict with energy conservation in its equation of m...

The radiative response of the classical electron is commonly described by the Lorentz-Abraham-Dirac (LAD) equation. Dirac's derivation of this equation is based on energy and momentum conservation laws and on regularization of the field singularities and infinite energies of the point charge by subtraction of certain quantities: "We ... shall try to get over difficulties associated with the infinite energy of the process by a process of direct omission or subtraction of unwan...

The problem of the electromagnetic radiation of an accelerated charged particle is one of the most controversial issues in Physics since the beginning of the last century, representing one of the most popular unsolved problems of the Modern Physics. Different equations of motion have been proposed throughout history for a point charge including the electromagnetic radiation emitted, but all these expressions show some limitations. An equation based on the principle of conserv...

The classical theory of radiating point-charges is revisited: the retarded potentials, fields, and currents are defined as nonlinear generalized functions. All calculations are made in a Colombeau algebra, and the spinor representations provided by the biquaternion formulation of classical electrodynamics are used to make all four-dimensional integrations exactly and in closed-form. The total rate of energy-momentum radiated by an arbitrarily moving relativistic point-charge ...

The dynamics of a radiating charge is one of the oldest unsettled problems in classical physics. The standard Lorentz-Abraham-Dirac (LAD) equation of motion is known to suffer from several pathologies and ambiguities. This paper briefly reviews these issues, and reports on a new model that fixes these difficulties in a natural way. This model is based on a hypothesis that there is an infinitesimal time delay between action and reaction. This can be related to Feynman's regula...

This paper is devoted to the analysis of the divergence of the electron self-energy in classical electrodynamics. To do so, we appeal to the theory of distributions and a method for obtaining corresponding extensions. At first sight, electrostatics implies a divergence once we treat the electron as a charged point particle. However, our construction shows that its self-energy turns out to be an undetermined constant upon renormalization. Appealing to empirical results we may ...