= Normalization of the electromagnetic dual tensor
{title2=$\widetilde F^{ab}=\tfrac12\epsilon^{abcd}F_{cd}$}
In oriented Minkowski coordinates with $(+---)$ signature and $\epsilon^{0123}=+1$, the conventional dual is $\widetilde F^{ab}=\tfrac12\epsilon^{abcd}F_{cd}$. For $F_{0i}=E_i$ and $F_{ij}=-\epsilon_{ijk}B_k$ in $c=1$ units, $\widetilde F^{ab}F_{ab}=-4\mathbf E\cdot\mathbf B$. A definition without the half produces twice this dual and contraction $-8\mathbf E\cdot\mathbf B$. The factor accounts for summing both orders of each antisymmetric index pair.
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