BIOT-SAVART-AMPERE LAW AND THE VACUUM FIELD B-(3)

It is shown that the longitudinal vacuum field B-(3) emerges from the Biot-Savart-Ampere law governing the motion of an electron with intrin sic spin moving at the speed of light, in which case the expression fo r B-(3) is identical with that obtained from the Dirac equation of one electron accelerated to the speed of light by an electromagnetic fiel d. Use of an O(3), non-Abelian, gauge geometry for B-(3) identifies th e quantized photon momentum Hbar kappa appearing in the Dirac equation with eA((0)), where e is the charge on the electron and A((0)) the am plitude of the vector potential. The condition Hbar kappa 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 fi eld.