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?

L. P. Horwitz,1 N. Katz,2 and O. Oron3

 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

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.