Abstract
It is shown that the longitudinal vacuum fieldB (3) emerges from the Biot-Savart-Ampère law governing the motion of an electron with intrinsic spin moving at the speed of light, in which case the expression forB (3) is identical with that obtained from the Dirac equation of one electron accelerated to the speed of light by an electromagnetic field. Use of an O(3), non-Abelian, gauge geometry forB (3) identifies the quantized photon momentum ħκ appearing in the Dirac equation witheA (0), wheree is the charge on the electron andA (0) the amplitude of the vector potential. The condition ħκ=eA (0) can be obtained in turn from the relativistic Hamilton-Jacobi equation of an electron accelerated to the speed of light by an electromagnetic field.
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Evans, M.W. The Biot-Savart-Ampère law and the vacuum fieldB (3) . Found Phys Lett 8, 381–388 (1995). https://doi.org/10.1007/BF02187818
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DOI: https://doi.org/10.1007/BF02187818