Subluminal and Superluminal Electromagnetic Waves and the Lepton Mass Spectrum

Rodrigues Jr., W. A.; Vaz Jr, J.

Subluminal and Superluminal Electromagnetic Waves and the Lepton Mass Spectrum

Authors

Description

Maxwell equation $\dirac F = 0$ for $F \in \sec \bwe^2 M \subset \sec \clif (M)$, where $\clif (M)$ is the Clifford bundle of differential forms, have subluminal and superluminal solutions characterized by $F^2 \neq 0$. We can write $F = ψγ_{21} \tilde ψ$ where $ψ\in \sec \clif^+(M)$. 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 $\dirac ψ=0$, $ψ\in \sec \clif^+ (M)$, is equivalent to a generalized Maxwell equation $\dirac F = J_{e} - γ_5 J_{m} = {\cal J}$. For $ψ= ψ^\uparrow$ a positive parity eigenstate, $j_e = 0$. Calling $ψ_e$ the solution corresponding to the electron, coming from $\dirac F_e =0$, we show that the NLDHE for $ψ$ such that $ψγ_{21} \tildeψ = F_e + F^{\uparrow}$ 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.
24 pages, KAPPROC style (Kluwer Ac. Pub. Proceedings) with named references. The Abstract to appear in the e-print archive list has been corrected. The main text is the same