Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 1 (2005), 012, 10 pages      math-ph/0511075      https://doi.org/10.3842/SIGMA.2005.012

Radiation Reaction, Renormalization and Poincaré Symmetry

Yurij Yaremko
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

Abstract
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.

Key words: classical electrodynamics; point-like charges; Poincaré invariance; conservation laws; renormalization procedure.

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