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Subluminal and Superluminal Electromagnetic Waves and the Lepton Mass Spectrum | | W. A. Rodrigues Jr.
; J. Vaz Jr
; | | Date: |
30 Jul 1996 | | Subject: | hep-th | | Abstract: | Maxwell equation $dirac F = 0$ for $F in sec we^2 M subset sec clif (M)$, where $clif (M)$ is the Clifford bundle of differential forms, have subluminal and superluminal solutions characterized by $F^2
eq 0$. We can write $F = psi gamma_{21} ilde psi$ where $psi in sec clif^+(M)$. We can show that $psi$ 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 $pi$). 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 $psi = psi^uparrow$ a positive parity eigenstate, $j_e = 0$. Calling $psi_e$ the solution corresponding to the electron, coming from $dirac F_e =0$, we show that the NLDHE for $psi$ such that $psi gamma_{21} ilde{psi} = F_e + F^{uparrow}$ gives a linear DHE for Takabayasi angles $pi/2$ and $3pi/2$ with the muon mass. The Tau mass can also be obtained with additional hypothesis. | | Source: | arXiv, hep-th/9607231 | | Services: | Forum | Review | PDF | Favorites | |
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