Electromagnetic field theory without divergence problems 1. The born legacy

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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.

Original languageEnglish (US)
Pages (from-to)1057-1122
Number of pages66
JournalJournal of Statistical Physics
Issue number1-4
StatePublished - Aug 2004

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Hamilton-Jacobi law of motion
  • Pauli principle
  • determinism: Maxwell-Born-Infeld field equations
  • electromagnetism: electromagnetic fields
  • permutability: configuration space
  • point charges
  • spacetime: special and general relativity


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