Gauge-theory Bianchi identity
= Gauge-theory Bianchi identity
{title2=$D_{[\mu}F_{\nu\rho]}=0$}
The <Jacobi identity> for <gauge covariant derivatives> gives $D_{[\mu}F_{\nu\rho]}=0$. In four dimensions this is $D_\mu\widetilde F^{\mu\nu}=0$, with $\widetilde F^{\mu\nu}=\frac12\varepsilon^{\mu\nu\rho\sigma}F_{\rho\sigma}$. It holds independently of the <Yang-Mills equations>.