Benedict Irwin edited Electromagnetism.tex  about 10 years ago

Commit id: a995e32d24d7eab6a4fa19c7d11c5f3106450ec2

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I_{\mu \nu}=Im_i[H_{\mu \nu}]=\partial_\mu B_\nu - \partial_\nu B_\mu \\  J_{\mu \nu}=Im_j[H_{\mu \nu}]=\partial_\mu \Gamma_\nu - \partial_\nu \Gamma_\mu \\  K_{\mu \nu}=Im_k[H_{\mu \nu}]=\partial_\mu \Delta_\nu - \partial_\nu \Delta_\mu   \end{equation}  This means that the real component $F_{\mu \nu}$ is equal to th regular EM tensor \begin{equation}  F_{\mu \nu} = \frac{1}{c} \begin{bmatrix}  0 E_x E_y E_z \\  -E_x 0 -cB_z cB_y \\  -E_y cB_z 0 -cB_x \\  -Ez -cB_y cB_x 0  \end{bmatrix}  \end{equation}  However, \begin{equation}  F^{\alpha \beta}=\eta^{\alpha \gamma}\eta^{\beta \delta}F_{\gamma \delta}  \end{equation}  Through explicit calculation this results in \begin{equation}  \end{equation}