= Dual electromagnetic field tensor
{title2=$\widetilde F^{\mu\nu}$}
The dual electromagnetic field tensor is obtained by applying the <Hodge star operator> to the <electromagnetic field tensor>. For metric signature $(+---)$ and $\epsilon^{0123}=+1$, define $\widetilde F^{\mu\nu}=\tfrac12\epsilon^{\mu\nu\rho\sigma}F_{\rho\sigma}$. With $F^{0i}=-E_i/c$ and $F^{ij}=-\epsilon_{ijk}B_k$, it has components $\widetilde F^{0i}=-B_i$ and $\widetilde F^{ij}=\epsilon_{ijk}E_k/c$. The homogeneous <Maxwell equations> become $\partial_\mu\widetilde F^{\mu\nu}=0$.
Back to article page
