Physics – Mathematical Physics
Scientific paper
2003-11-20
J.Stat.Phys. vol.116, p.1123-1159 (2004)
Physics
Mathematical Physics
Corrections at galley stage incorporated (mostly minor corrections, except for a blunder in the estimate of the error term U t
Scientific paper
10.1023/B:JOSS.0000037251.24558.
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.
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