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 ≠ 0. We can write F = ψγ 21 ψγ where ψ ∊ sec Cl+ (M). We can show that ψ satisfies a non linear Dirac-Hestenes 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 = J e − γ 5 J m = J. For ψ = ψ ↑ a positive parity eigenstate, J e = 0. Calling ψ e the solution corresponding to the electron, coming from ∂F e = 0, we show that the NLDHE for ψ such that ψγ 21 ψγ = F e + 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.