Quantum mechanical probability current as electromagnetic 4-current from topological EM fields

摘要

Starting from a complex 4-potential A = αdβ we show that the 4-current density in electromagnetism and the probability current density in relativistic quantum mechanics are of identical form. With the Dirac-Clifford algebra Cl_(1,3) as mathematical basis, the given 4-potential allows topological solutions of the fields, quite similar to Bateman's construction, but with a double field solution that was overlooked previously. A more general null-vector condition is found and wave-functions of charged and neutral particles appear as topological configurations of the electromagnetic fields.