Benedict Irwin edited Electromagnetism.tex  about 10 years ago

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\end{equation}  %But But  with the hypercomplex components it is clear that $H_{\mu \nu} = F_{\mu \nu} +I_{\mu \nu}i + J_{\mu \nu}j + K_{\mu \nu}k \nu}k$  where \begin{equation}  F_{\mu \nu}+Re[H_{\mu \nu}=Re[H_{\mu  \nu}]=\partial_\mu A_\nu - \partial_\nu A_\mu \\ I_{\mu \nu}+Im_i[H_{\mu \nu}=Im_i[H_{\mu  \nu}]=\partial_\mu B_\nu - \partial_\nu B_\mu \\ J_{\mu \nu}+Im_j[H_{\mu \nu}=Im_j[H_{\mu  \nu}]=\partial_\mu \Gamma_\nu - \partial_\nu \Gamma_\mu \\ K_{\mu \nu}+Im_k[H_{\mu \nu}=Im_k[H_{\mu  \nu}]=\partial_\mu \Delta_\nu - \partial_\nu \Delta_\mu \end{equation}