Journal of Statistical Physics, Vol. 116, Nos. 1/4, August 2004. p. 1123-1159.
Classical electrodynamics based on the Maxwell-Born-Infeld field equations coupled with a Hamilton—Jacobi law of point charge motion is partially quantized. The Hamilton—Jacobi phase function is supplemented by a dynamical amplitude field on configuration space. Both together combine into a single complex wave function satisfying a relativistic Klein-Gordon equation that is self-consistently coupled to the evolution equations for the point charges and the electromagnetic fields. Radiation-free stationary states exist. The hydrogen spectrum is discussed in some detail. Upper bounds for Born's "aether constant" are obtained. In the limit of small velocities of and negligible radiation from the point charges, the model reduces to Schrodinger's equation with Coulomb Hamiltonian, coupled with the de Broglie-Bohm guiding equation.