A generalized electromagnetic theory for the mass spectrum of neutrinos

E. Capelas de Oliveira, W.A. Rodrigues Jr., J. Vaz Jr.1


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.


  1. W. A. Rodrigues, Jr., Int. J. Math. and Math, Sci. 2003, 2707–2734 (2003); math-ph/0212034.
  2. W. A. Rodrigues, Jr. and E. Capelas de Oliveira, The Many Faces of Maxwell, Dirac and Einstein Equations. A Clifford Bundle Approach. Lecture Notes in Physics 722 (Springer, Heidelberg, 2007).
  3. J. Vaz, Jr. and W. A. Rodrigues, Jr., Int. J. Theor. Phys. 32, 945–955 (1993).
  4. E. Capelas de Oliveira, W. A. Rodrigues, Jr., D. S. Thober, and A. L. Xavier, Jr., Phys. Lett. A 284, 296–303 (2001).
  5. W. A. Rodrigues, Jr., D. S. Thober, and A. L. Xavier, Jr., Phys. Lett. A 284, 217–224 (2001).
  6. R. A. Mosna and W. A. Rodrigues, Jr., J. Math. Phys. 45, 2945–2966 (2004); math-ph/0212033.
  7. W. A. Rodrigues, Jr. and J. Vaz, Jr., Found. Phys. 28, 789–814 (1998).
  8. S. A. Thomas, F. B. Abdalla, and O. Lahav, Phys.Rev. Lett. 105, 031301 (2010).
  9. K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010).
  10. G. Lochak, Int. J. Theor. Phys. 24, 1019–1050 (1985).
  11. E. Capelas de Oliveira, W. A. Rodrigues, Jr., and J. Vaz, Jr., Elko Spinor Fields and Massive Magnetic Like Monopoles, arXiv: 1306.4645.
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