# 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

### Abstract

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*^{∞} = - *g*J with a current J as a source and such that the Lorentz force on the current is null. We first identify a solution where *J*_{m} = - γ^{5}J 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 F_{0} 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 F_{0} satisfies a Dirac-like equation for a bradyonic neutrino under the *ansatz* that the current is *ce*^{λγ5}*g*ψγ^{0}ψ˜ 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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