Abstract
It is shown that an approach to quantum phenomena in which charged particles are treated as macroscopically extended periodic disturbances in a nonlinear c-number field, interacting with each other via massless excitations of that field, leads almost uniquely to the five basic equations of classical electrodynamics: the Lorentz force law and Maxwell's equations. The fundamental electromagnetic quantity in this approach is the 4-vector potential Aα—interpreted absolutely as a measure of the local shift of each particle off its mass shell—rather than theE andB fields, and it thus provides a new viewpoint on the questions of Aharonov-Bohm phase shifts, the existence of magnetic monopoles, and the role of gauge invariance.
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Wignall, J.W.G. Maxwell electrodynamics from a theory of macroscopically extended particles. Found Phys 20, 139–158 (1990). https://doi.org/10.1007/BF00731644
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DOI: https://doi.org/10.1007/BF00731644