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.