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Subluminal and Superluminal Electromagnetic Waves and the Lepton Mass Spectrum
High Energy Physics - Theory · Submitted 30 Jul 1996
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Calling $\psi_e$ the solution corresponding to the electron, coming from $\dirac F_e =0$, we show that the NLDHE for $\psi$ such that $\psi \gamma_{21} \tilde{\psi} = F_e + F^{\uparrow}$ gives a linear DHE for Takabayasi angles $\pi/2$ and $3\pi/2$ with the muon mass.
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The abstract, sentence by sentence
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 $F = \psi \gamma_{21} \tilde \psi$ 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 $\psi \gamma_{21} \tilde{\psi} = F_e + F^{\uparrow}$ gives a linear DHE for Takabayasi angles $\pi/2$ and $3\pi/2$ with the muon mass. The Tau mass can also be obtained with additional hypothesis.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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 $F^2 \neq 0$. | background 0.64 | 0.22 | 0.22 | asserted 1.00 |
| s1 | We can write $F = \psi \gamma_{21} \tilde \psi$ where $\psi \in \sec \clif^+(M)$. | method 0.68 | 0.61 | 0.05 | asserted 0.54 |
| s2 | We can show that $\psi$ satisfies a non linear Dirac-Hestenes Equation (NLDHE). | result 0.68 | 0.89 | 0.09 | asserted 0.95 |
| s3 | Under reasonable assumptions we can reduce the NLDHE to the linear Dirac-Hestenes Equation (DHE). | result 0.68 | 0.84 | 0.12 | asserted 0.89 |
| s4 | This happens for constant values of the Takabayasi angle ($0$ or $\pi$). | result 0.90 | 0.75 | 0.06 | asserted 0.98 |
| s5 | The massless Dirac equation $\dirac \psi =0$, $\psi \in \sec \clif^+ (M)$, is equivalent to a generalized Maxwell equation $\dirac F = J_{e} - \gamma_5 J_{m} = {\cal J}$. | result 0.65 | 0.48 | 0.14 | asserted 1.00 |
| s6 | For $\psi = \psi^\uparrow$ a positive parity eigenstate, $j_e = 0$. | result 0.98 | 0.76 | 0.04 | asserted 1.00 |
| s7 | Calling $\psi_e$ the solution corresponding to the electron, coming from $\dirac F_e =0$, we show that the NLDHE for $\psi$ such that $\psi \gamma_{21} \tilde{\psi} = F_e + F^{\uparrow}$ gives a linear DHE for Takabayasi angles $\pi/2$ and $3\pi/2$ with the muon mass. | result 0.97 | 0.90 | 0.55 | asserted 1.00 |
| s8 | The Tau mass can also be obtained with additional hypothesis. | result 0.85 | 0.74 | 0.12 | hedged possibility 0.81 |
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Original abstract
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 $F = \psi \gamma_{21} \tilde \psi$ 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 $\psi \gamma_{21} \tilde{\psi} = F_e + F^{\uparrow}$ gives a linear DHE for Takabayasi angles $\pi/2$ and $3\pi/2$ with the muon mass. The Tau mass can also be obtained with additional hypothesis.
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