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Benedict Irwin edited Electromagnetism.tex
about 10 years ago
Commit id: 2b65df71df7efc62e8cb4700433c765c5fec13b0
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But with the hypercomplex components it is clear that $H_{\mu \nu} = F_{\mu \nu} +I_{\mu \nu}i + J_{\mu \nu}j + K_{\mu \nu}k where
\begin{equation}
%F_{\mu F_{\mu \nu}+Re[H_{\mu \nu}]=\partial_\mu A_\nu - \partial_\nu A_\mu \\
%I_{\mu I_{\mu \nu}+Im_i[H_{\mu \nu}]=\partial_\mu B_\nu - \partial_\nu B_\mu \\
%J_{\mu J_{\mu \nu}+Im_j[H_{\mu \nu}]=\partial_\mu \Gamma_\nu - \partial_\nu \Gamma_\mu \\
%K_{\mu K_{\mu \nu}+Im_k[H_{\mu \nu}]=\partial_\mu \Delta_\nu - \partial_\nu \Delta_\mu
\end{equation}