The Lorentz-Dirac equation in complex space-time

Abstract

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.