Discrete Dynamics in Nature and Society
Volume 2004 (2004), Issue 1, Pages 179-204
doi:10.1155/S1026022604401034
Could the classical relativistic electron be a strange attractor?
1School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv 69978, Israel
2Department of Physics, Bar-Ilan University, Ramat Gan 52900, Israel
3School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv 69978, Israel
Received 5 January 2004
Copyright © 2004 L. P. Horwitz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We review the formulation of the problem of the electromagnetic
self-interaction of a relativistic charged particle in the
framework of the manifestly covariant classical mechanics of
Stueckelberg, Horwitz, and Piron. The gauge fields of this theory,
in general, cause the mass of the particle to change. We show
that the nonlinear Lorentz force equation for the
self-interaction resulting from the expansion of Green's function
has chaotic solutions. We study the autonomous equation for the
off-shell particle mass here, for which the effective charged
particle mass achieves a macroscopic average value determined by
what appears to be a strange attractor.