417 research outputs found
Radiation Reaction, Renormalization and Poincar\'e Symmetry
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.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Self force in 2+1 electrodynamics
The radiation reaction problem for an electric charge moving in flat
space-time of three dimensions is discussed. The divergences stemming from the
pointness of the particle are studied. A consistent regularization procedure is
proposed, which exploits the Poincar\'e invariance of the theory. Effective
equation of motion of radiating charge in an external electromagnetic field is
obtained via the consideration of energy-momentum and angular momentum
conservation. This equation includes the effect of the particle's own field.
The radiation reaction is determined by the Lorentz force of point-like charge
acting upon itself plus a non-local term which provides finiteness of the
self-action.Comment: 20 pages, 3 figure
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