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, havesubluminal and superluminal solutions characterized by $F^2 \neq 0$. We canwrite $F = \psi \gamma_{21} \tilde \psi$ where $\psi \in \sec \clif^+(M)$. Wecan show that $\psi$ satisfies a non linear Dirac-Hestenes Equation (NLDHE).Under reasonable assumptions we can reduce the NLDHE to the linearDirac-Hestenes Equation (DHE). This happens for constant values of theTakabayasi angle ($0$ or $\pi$). The massless Dirac equation $\dirac \psi =0$,$\psi \in \sec \clif^+ (M)$, is equivalent to a generalized Maxwell equation$\dirac F = J_{e} - \gamma_5 J_{m} = {\cal J}$. For $\psi = \psi^\uparrow$ apositive parity eigenstate, $j_e = 0$. Calling $\psi_e$ the solutioncorresponding to the electron, coming from $\dirac F_e =0$, we show that theNLDHE for $\psi$ such that $\psi \gamma_{21} \tilde{\psi} = F_e + F^{\uparrow}$gives a linear DHE for Takabayasi angles $\pi/2$ and $3\pi/2$ with the muonmass. The Tau mass can also be obtained with additional hypothesis.
展开▼