  A hypothetical equation of motion is proposed for Kerr-Newman particles. It
is obtained by analytic continuation of the Lorentz-Dirac equation into complex
space-time. A new class of "runaway" solutions are found which are similar to
Zitterbewegung. Electromagnetic fields generated by these motions are studied,
and it is found that the retarded times are multi-sheeted functions of the
field points. This leads to non-uniqueness for the generated fields. It is
found that with fixed weighting factors for these multiple roots, the solutions
radiate electromagnetic energy. If the weighting factors are allowed to be
position dependent, however, then it is possible to suppress radiation by
solving a differential equation for these factors which ensures that the
solution is a non-radiating electromagnetic source. Motion in response to
external forces are also considered. Radiation suppression is possible here too
in some cases. These results are relevant for the idea that Kerr-Newman
solutions provide insight into elementary particles and into emergent quantum
mechanics.
