  Complexified Lienard-Wiechert potentials simplify the mathematics of
Kerr-Newman particles. Here we constrain them by fiat to move along Bohmian
trajectories to see if anything interesting occurs, as their equations of
motion are not known. A covariant theory due to Stueckelberg is used. This
paper deviates from the traditional Bohmian interpretation of quantum mechanics
since the electromagnetic interactions of Kerr- Newman particles are dictated
by general relativity. A Gaussian wave function is used to produce the Bohmian
trajectories, which are found to be multi-valued. A generalized analytic
continuation (GAN) is introduced which leads to an infinite number of
trajectories. These include the entire set of Bohmian trajectories. This leads
to multiple retarded times which come into play in complex space-time. If one
weights these trajectories by their natural Bohmian weighting factors, then it
is found that the particles do not radiate, that they are extended, and that
they can have a finite electrostatic self energy, thus avoiding the usual
divergence of the charged point particle. This effort does not in any way
criticize or downplay the traditional Bohmian interpretation which does not
assume the standard electromagnetic coupling to charged particles, but it
suggests that a hybridization of Kerr-Newman particle theory with Bohmian
mechanics might lead to interesting new physics, and maybe even the possibility
of emergent quantum mechanics.
