Authors: Gary Osborn
In the Aharonov-Bohm effect for a magnetic solenoid a moving charged particle seems to be influenced by the 4-potential in a region where there are no fields in the laboratory frame of reference. The 4-potential should be transformed to the frame of reference of the particle before computing the fields. There is an E field in its frame of reference. The field accelerates a moving charged particle. One of the components of the acceleration vector is in the same direction as the particle's velocity in the first frame of reference. The resulting longitudinal displacement in the path integral, when scaled in units of the de Broglie wavelength for the particle, is approximately the same as the phase of the Aharonov-Bohm solution for long paths. The scalar solution does not require transformation. It follows from the static Coulomb solution and the Newton equations.
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