Normalization of the electromagnetic dual tensor (${\tilde{F}}^{ab}=\frac{1}{2}{ϵ}^{abcd}{F}_{cd}$)

In oriented Minkowski coordinates with $(+---)$ signature and ${ϵ}^{0123}=+1$, the conventional dual is ${\tilde{F}}^{ab}=\frac{1}{2}{ϵ}^{abcd}{F}_{cd}$. For $F_{0i}=E_i$ and $F_{ij}=-{ϵ}_{ijk}{B}_k$ in $c=1$ units, ${\tilde{F}}^{ab}{F}_{ab}=-4\mathbf{E}\cdot \mathbf{B}$. 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.