Journal of Statistical Physics

, Volume 116, Issue 1–4, pp 1057–1122

Electromagnetic Field Theory Without Divergence Problems 1. The Born Legacy

  • Michael K.-H. Kiessling
Article

Abstract

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.

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

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Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • Michael K.-H. Kiessling
    • 1
  1. 1.Department of Mathematics, RutgersThe State University of New JerseyPiscataway

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