  The classical Maxwell--Born--Infeld field equations coupled with a
Hamilton--Jacobi law of point charge motion are partially quantized by coupling
the Hamilton-Jacobi phase function with an amplitude function, which combines
with the phase function into a single complex wave function satisfying a
relativistic Klein--Gordon equation self-consistently coupled to the evolution
equations for the electromagnetic fields with generic point source (explicitly
worked out for one particle; options for many particles briefly discussed).
Radiation-free stationary states exist. The hydrogen spectrum with infinitely
massive nucleus is discussed in some detail and upper estimates for Born's
`aether constant' obtained. In the nonrelativistic limit the model reduces to
the de-Broglie--Bohm formulation of quantum mechanics.
