Subluminal and Superluminal Electromagnetic Waves and the Lepton Mass Spectrum

Maxwell equation ∂F = 0 for F ∈ sec ∧2 M ⊂ sec Cl(M), where Cl(M) is the Clifford bundle of differential forms, have subluminal and superluminal solutions characterized by F 2 6= 0. We can write F = ψγ21ψ̃ where ψ ∈ sec Cl(M). We can show that ψ satisfies a non linear DiracHestenes Equation (NLDHE). Under reasonable assumptions we can reduce the NLDHE to the linear Dirac-Hestenes Equation (DHE). This happens for constant values of the Takabayasi angle (0 or π). The massless Dirac equation ∂ψ = 0, ψ ∈ sec Cl(M), is equivalent to a generalized Maxwell equation ∂F = Je − γ5Jm = J . For ψ = ψ a positive parity eigenstate, je = 0. Calling ψe the solution corresponding to the electron, coming from ∂Fe = 0, we show that the NLDHE for ψ such that ψγ21ψ̃ = Fe +F ↑ gives a linear DHE for Takabayasi angles π/2 and 3π/2 with the muon mass. The Tau mass can also be obtained with additional hypothesis.