Accelerating Charge: Add-Ons to Rest Mass and Field Energy

We present—in the framework of classical theory—a self-consistent derivation scheme which produces equations for the calculation of add-ons to the full field energy and to the effective mass of a charge moving with acceleration, which may be practically used for analyses in various scenarios. The charge is treated as a quasi-point-like charge; this helps to resolve the complications of the “infinite” electromagnetic energy, which are avoided by the procedure of slightly “spreading” the charge. As a result, the concept of the size of the particle takes a straightforward physical interpretation. Indeed, it is within the charge spread, at scales smaller than Compton’s length, where the quantum-field-mechanics approach to be applied. Beyond this region, no “infinite” tails of quantities accumulate. The seeming divergences of the integrals at the upper limits are not physical if one takes into account that the charge moves with acceleration only for a finite duration of time; every real physical process has its beginning and its end. The key focus of this paper is on the methodological aspects of the calculations.