A generalized electromagnetic theory for the mass spectrum of neutrinos
E. Capelas de Oliveira, W.A. Rodrigues Jr., J. Vaz Jr.1
(1) Institute of Mathematics, Statistics and Scientific Computation IMECC-UNICAMP, 13083-859, Campinas, SP, Brazil
In previous papers it was shown that solutions of Weyl equation that are eigenstates of the parity operator describe a coupled pair of a monopole anti-monopole system. These results suggest to seek a solution of the Maxwell equation ∂F∞ = - gJ with a current J as a source and such that the Lorentz force on the current is null. We first identify a solution where Jm = - γ5J is a spacelike field. More surprisingly we find that there exists a solution F of the free Maxwell ∂F = 0 that is equivalent to the inhomogeneous equation for F∞. Once this result is proved, it suggests by itself to seek more general (subluminal and even superluminal) solutions F of the free Maxwell equation equivalent to an inhomogeneous Maxwell equation for a field F0 with a current term as a source which may be a timelike or spacelike field. We exhibit one such subluminal solution, for which the Dirac-Hestenes spinor field ψ associated with the electromagnetic field F0 satisfies a Dirac-like equation for a bradyonic neutrino under the ansatz that the current is ceλγ5gψγ0ψ˜ with g the quantum of magnetic charge and λ a constant to be determined in such a way that the auto-force is zero. Together with Dirac's quantization condition this gives a quantized mass spectrum for neutrinos, with masses of the different flavor neutrinos being of the same order of magnitude, which is in accord with recent experimental findings.
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