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

An attempt is made to avoid the difficulty of the infinite reaction of the electron on itself, which occurs in quantum electrodynamics, by introducing difference equations instead of differential equations. This vision allows the difficulty of the relativistic wave equation emphasised by Klein, for example, to be essentially eliminated.

We present here the extended-object approach for the explanation and calculation of the self-force phenomenon. In this approach, one considers a charged extended object of a finite size $\epsilon$ that accelerates in a nontrivial manner, and calculates the total force exerted on it by the electromagnetic field (whose source is the charged object itself). We show that at the limit $\epsilon \to 0$ this overall electromagnetic field yields a universal result, independent on the...

The usual radiation self-force of a point charge is obtained in a mathematically exact way and it is pointed out to that this does not call forth that the spacetime motion of a point charge obeys the Lorentz--Abraham--Dirac equation.

We present a pedagogical review of old inconsistencies of Classical Electrodynamics and of some new ideas that solve them. Problems with the electron equation of motion and with the non-integrable singularity of its self-field energy tensor are well known. They are consequences, we show, of neglecting terms that are null off the charge world-line but that give a non null contribution on its world-line. The electron self-field energy tensor is integrable without the use of any...

We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuum-field structure. We analyze the models of the vacuum field medium and charged point particle dynamics using the developed field theory concepts. There is also described a new approach to the classical Maxwell theory based on the derived and newly interpreted basic equations making use of the vacuum field theory approach. In par...

While he derived the equation for the radiation force, Dirac (1938) mentioned a possibility to use different choices for the 4-momentum of an emitting electron. Particularly, the 4-momentum could be non-colinear to the electron 4-velocity. This ambiguity in the electron 4-momentum allows us to assume that the mass of emitting electron may be an operator, or, at least, a 4-tensor instead of being the usually assumed scalar, which relates the 4-velocity of a bare charge to the ...

In 1892 H.A. Lorentz started the search for a classical equation of motion for pointlike charged particles that takes into account the radiation reaction force. This search culminated in the Lorentz-Abraham-Dirac equation of motion, which is not satisfactory since it exhibits self-acceleration causing runaway solutions. In spite of ongoing efforts for more than a century, there is yet no acceptable classical equation of motion for a pointlike charge, cf. the recent paper by R...

This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz-Dirac equation for a single point particle a simple model is proposed for a charged continuum interacting self-consistently with the Maxwell field in vacuo. The model is developed using intrinsic tensor field theory and exploits to the full the symmetry and light-cone structure of Min...

A model is proposed for the classical electron as a point charge with finite electromagnetic self-energy. Modifications of the Reissner-Nordstr{\o}m (spin 0) and Kerr-Newman (spin 1/2) solutions of the Einstein-Maxwell equations are derived. It is conjectured that spacetime curvature very close to the point charge deforms the electric and magnetic fields such as to reduce the self-energy to a finite value by means of Hawking polarization of the vacuum, much like that around a...

We revisit in the framework of the classical theory the problem of the accelerated motion of an electron, taking into account the effect of the radiation emission. We present results for the momentum and energy of the electromagnetic field of an accelerated electron for a spatial region excluding a vicinity of the electron and a procedure to compensate their singularities in the limit of the point electron. From them we infer expressions for the observables momentum and energ...