TY - JOUR

T1 - Electromagnetic field theory without divergence problems 2. A least invasively quantized theory

AU - Kiessling, Michael K.H.

N1 - Funding Information:
This work began in early 1992 when the author held a German-Dartmouth distinguished visiting professorship at Dartmouth College. It was supported in the past two years by NSF Grant DMS-0103808. I am indebted to many individuals, but I am most grateful to S. Goldstein and H. Spohn for many invaluable scientific discussions about electromagnetism and quantum theory. I also thank S. Chanillo for Moser’s theorem, and J. Taylor for his insights into the Fermi bundle. I owe very special thanks to S. Goldstein and, especially, to R. Tumulka for their helpful comments and penetrating criticisms of an earlier version of this paper, which prompted me to improve and clarify the presentation. My sincere thanks go also to the five referees for their favorable reactions to this nonmainstream paper and their helpful suggestions. I thank T. Dorlas for sending me copies of Schrödinger’s Dublin papers, and Y. Brenier and I. Białynicki-Birula for bringing their more recent works to my attention after the first version of this paper was circulated.

PY - 2004/8

Y1 - 2004/8

N2 - 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 Schrödinger's equation with Coulomb Hamiltonian, coupled with the de Broglie-Bohm guiding equation.

AB - 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 Schrödinger's equation with Coulomb Hamiltonian, coupled with the de Broglie-Bohm guiding equation.

KW - determinism: Maxwell-Born-Infeld field equations, de Broglie-Bohm law of quantum motion, Klein-Gordon equation

KW - electromagnetism: electromagnetic fields, point charges, wave functions

KW - spacetime: special relativity, space-like foliations

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U2 - 10.1023/B:JOSS.0000037251.24558.5c

DO - 10.1023/B:JOSS.0000037251.24558.5c

M3 - Article

AN - SCOPUS:4344714039

VL - 116

SP - 1123

EP - 1159

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-4

ER -