SIGMA 1 (2005), 012, 10 pages math-ph/0511075
Radiation Reaction, Renormalization and Poincaré Symmetry
Institute for Condensed Matter Physics of National Academy of Sciences of Ukraine,
1 Svientsitskii Str., Lviv, 79011 Ukraine
Received July 08, 2005, in final form October 23, 2005; Published online November 01, 2005
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 Poincaré-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.
classical electrodynamics; point-like charges;
Poincaré invariance; conservation laws; renormalization procedure.
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