  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 non-linear Lorentz force equation for the
self-interaction resulting from the expansion of the 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.
