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Generalized Maxwell equations and quantum mechanics. I: Dirac equation for the free electron. (English) Zbl 0705.35137
Using an appropriate formalism elaborated in some previous works the author establishes that the Dirac equation for the free electron is equivalent to the Maxwell equations for an electromagnetic field generated by two currents: one electric like and one magnetic monopolar. As a by-product one then gets nonlinear generalizations of Maxwell’s and Dirac’s equation which have interesting physical interpretations concerning the nature of the electron mass and of the magnetic monopole mass. In the end it is shown that the nonlinear Dirac equation reduces to the ordinary one under suitable approximations.
Reviewer: L.Nicolaescu

MSC:
35Q60 PDEs in connection with optics and electromagnetic theory
35Q40 PDEs in connection with quantum mechanics
81V10 Electromagnetic interaction; quantum electrodynamics
81R25 Spinor and twistor methods applied to problems in quantum theory
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