Institute for Condensed Matter Physics of NAS of Ukraine,

1 Svientsitskii Str.,

79011 Lviv,

UKRAINE

E-mail: yar@ph.icmp.lviv.ua

**Radiation reaction, renormalization and Poincare symmetry**

**Abstract:**

We consider the self-action problem in classical electrodynamics of
a massive point-like charge as well as 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 Poincare-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 on 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.