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

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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.

Original languageEnglish (US)
Pages (from-to)1123-1159
Number of pages37
JournalJournal of Statistical Physics
Issue number1-4
StatePublished - Aug 2004

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • determinism: Maxwell-Born-Infeld field equations, de Broglie-Bohm law of quantum motion, Klein-Gordon equation
  • electromagnetism: electromagnetic fields, point charges, wave functions
  • spacetime: special relativity, space-like foliations


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