= Index conventions for the electromagnetic field tensor
Choose coordinates $x^\mu=(ct,\mathbf x)$ and <Minkowski metric> $\eta=\operatorname{diag}(1,-1,-1,-1)$. With the convention $F^{0i}=-E_i/c$ and $F^{ij}=-\epsilon_{ijk}B_k$, lowering both <tensor> indices gives $F_{0i}=+E_i/c$ while leaving $F_{ij}=F^{ij}$. An array with all upper indices cannot be used unchanged as the corresponding array with all lower indices. The propagation <Lorentz four-vector> $n^\mu=(1,\mathbf s)$ for unit spatial direction $\mathbf s$ similarly has $n_\mu=(1,-\mathbf s)$. These signs matter in contractions that encode <Maxwell equations>.
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