Radiation Reaction, Renormalization and Poincar\'e Symmetry We consider the self-action problem in classical electrodynamics of a massive point-like charge, as well as of a massless one. A consistent regularization procedure is proposed, which exploits the symmetry properties of the theory. The radiation reaction forces in both 4D and 6D are derived. It is demonstrated that the Poincar\'e-invariant six-dimensional electrodynamics of the massive charge is renormalizable theory. Unlike the massive case, the rates of radiated energy-momentum tend to infinity whenever the source is accelerated. The external electromagnetic fields, which do not change the velocity of the particle, admit only its presence within the interaction area. The effective equation of motion is the equation for eigenvalues and eigenvectors of the electromagnetic tensor. The interference part of energy-momentum radiated by two massive point charges arbitrarily moving in flat spacetime is evaluated. It is shown that the sum of work done by Lorentz forces of charges acting on one another exhausts the effect of combination of outgoing electromagnetic waves generated by the charges.

The Self-Force of a Charged Particle in Classical Electrodynamics with a Cut-off We discuss, in the context of classical electrodynamics with a Lorentz invariant cut-off at short distances, the self-force acting on a point charged particle. It follows that the electromagnetic mass of the point charge occurs in the equation of motion in a form consistent with special relativity. 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. Published as: Int.J.Mod.Phys. B13 (1999) 315-324 DOI: 10.1142/S0217979299000199 arXiv categories: physics.class-ph hep-ph hep-th

the self-force on a moving mirror. The force is proportional to the square of the object's charge, multiplied by the jerk that it is experiencing. (Jerk In the physics of electromagnetism, the Abraham–Lorentz force (also known as the Lorentz–Abraham force) is the reaction force on an accelerating charged particle caused by the particle emitting electromagnetic radiation by self-interaction. It is also called the radiation reaction force, the radiation damping force, or the self-force. It is named after the physicists Max Abraham and Hendrik Lore The difficulties presented by this problem touch one of the most fundamental aspects of physics, the nature of the elementary particle. Although partial solutions, workable within limited areas, can be given, the basic problem…

Motions of Classical Charged Tachyons It is shown by numerical simulation that classical charged tachyons have self-orbiting helical solutions in a narrow neighborhood of certain discrete values for the velocity when the electromagnetic interaction is described by Feynman-Wheeler electrodynamics. The force rapidly oscillates between attractive and repulsive as a function of velocity in this neighborhood. Causal electrodynamics is also considered, and in this case it is found that when the force is attractive the tachyon loses energy to radiation. Only certain narrow ranges of velocity give attractive forces, and a geometrical derivation of these special velocities is given. Possible implications of these results for hidden variable theories of quantum mechanics are conjectured. Published as: Phys.Essays 14 (2001) 66-75 arXiv categories: quant-ph

Variational principle and energy-momentum tensor for relativistic Electrodynamics of point charges We give a new representation as tempered distribution for the energy-momentum tensor of a system of charged point-particles, which is free from divergent self-interactions, manifestly Lorentz-invariant and symmetric, and conserved. We present a covariant action for this system, that gives rise to the known Lorentz-Dirac equations for the particles and entails, via Noether theorem, this energy-momentum tensor. Our action is obtained from the standard action for classical Electrodynamics, by means of a new Lorentz-invariant regularization procedure, followed by a renormalization. The method introduced here extends naturally to charged p-branes and arbitrary dimensions. Published as: AnnalsPhys.322:1162-1190,2007 DOI: 10.1016/j.aop.2006.07.002 arXiv categories: hep-th

In electrical engineering, electric charges usually move at speeds substantially slower than the speed of light. Therefore, relativistic mechanics and the Lorentz transformation are rarely applied; instead, the much simpler Newtonian mechanics and the Galilean transformation are used. This approximation is hoped to yield useful results. In this article, the exact solution of Maxwell's equations for arbitrarily moving point charges is used to demonstrate that this approximation is not suitable for point charges, even if they move extremely slowly. Nevertheless, in electrical engineering, great practical demand exists for a functioning and consistent electrodynamic model for non-relativistic point charges. This article presents such a model and demonstrates that it ensures the universal constancy of the speed of light for all receiving antennas, while satisfying the Galilean principle of relativity regarding the point charges, and being compatible with Newtonian mechanics and the classical Newtonian conservation of momentum. The framework can describe electromagnetic waves as well as all static and quasistatic effects with excellent quality if they are generated by non-relativistic point charges. The framework is based on the exact solution of Maxwell's equations for arbitrarily moving point charges and a simplified Lorentz force law, which has been calibrated so that the force for slow velocities matches Ampère's original force law and thus fulfills the predictions of magnetostatics and quasistatics.

On the Electric and Magnetic Effects produced by the Motion of Electrified Bodies ← On the Electric and Magnetic Effects produced by the Motion of Electrified Bodies ( 1881 ) by Joseph John Thomson → related portals : Relativity sister projects : Wikidata item Philosophical Magazine, 1881, 5 11 (68): 229-249, Online 415323 On the Electric and Magnetic Effects produced by the Motion of Electrified Bodies 1881 Joseph John Thomson ​ § 1. IN the interesting experiments recently made by Mr. Crookes (Phil. Trans. 1879, parts 1 and 2) and Dr. Goldstein (Phil. Mag. Sept. and Oct. 1880) on "Electric Discharges in High Vacua," particles of matter highly charged with electricity and moving with great velocities form a prominent feature in the phenomena; and a large portion of the investigations consists of experiments on the action of such particles on each other, and their behaviour when under the influence of a magnet. It seems therefore to be of some interest, both as a test of the theory and as a guide to future experiments, to take some theory of electrical action and find what, according to it, is the force existing between two moving electrified bodies, what is the magnetic force produced by such a moving body, and in what way the body is affected by a magnet. The following paper is an attempt to solve these problems, taking as the basis Maxwell's theory that variations in the electric displacement in a dielectric produce effects analogous to those produced by ordinary currents f