TY - JOUR

T1 - Electromagnetic field theory without divergence problems 1. The born legacy

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 - Born's quest for the elusive divergence problem-free quantum theory of electromagnetism led to the important discovery of the nonlinear Maxwell-Born-Infeld equations for the classical electromagnetic fields, the sources of which are classical point charges in motion. The law of motion for these point charges has however been missing, because the Lorentz self-force in the relativistic Newtonian (formal) law of motion is ill-defined in magnitude and direction. In the present paper it is shown that a relativistic Hamilton-Jacobi type law of point charge motion can be consistently coupled with the nonlinear Maxwell-Born-Infeld field equations to obtain a well-defined relativistic classical electrodynamics with point charges. Curiously, while the point charges are spinless, the Pauli principle for bosons can be incorporated. Born's reasoning for calculating the value of his aether constant is re-assessed and found to be inconclusive.

AB - Born's quest for the elusive divergence problem-free quantum theory of electromagnetism led to the important discovery of the nonlinear Maxwell-Born-Infeld equations for the classical electromagnetic fields, the sources of which are classical point charges in motion. The law of motion for these point charges has however been missing, because the Lorentz self-force in the relativistic Newtonian (formal) law of motion is ill-defined in magnitude and direction. In the present paper it is shown that a relativistic Hamilton-Jacobi type law of point charge motion can be consistently coupled with the nonlinear Maxwell-Born-Infeld field equations to obtain a well-defined relativistic classical electrodynamics with point charges. Curiously, while the point charges are spinless, the Pauli principle for bosons can be incorporated. Born's reasoning for calculating the value of his aether constant is re-assessed and found to be inconclusive.

KW - Hamilton-Jacobi law of motion

KW - Pauli principle

KW - determinism: Maxwell-Born-Infeld field equations

KW - electromagnetism: electromagnetic fields

KW - permutability: configuration space

KW - point charges

KW - spacetime: special and general relativity

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U2 - 10.1023/B:JOSS.0000037250.72634.2a

DO - 10.1023/B:JOSS.0000037250.72634.2a

M3 - Review article

AN - SCOPUS:4344661816

VL - 116

SP - 1057

EP - 1122

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-4

ER -