= Covariant wave equation for the Yang-Mills field strength
{title2=$D^\rho D_\rho F_{\mu\nu}=2[F_\mu{}^\rho,F_{\nu\rho}]$}
Apply $D^\rho$ to the <gauge-theory Bianchi identity> and commute it through the other derivatives using $[D_\mu,D_\nu]X=[F_{\mu\nu},X]$. The <Yang-Mills equations> remove the differentiated divergences. The two remaining <commutator> terms both equal $[F_\mu{}^\rho,F_{\nu\rho}]$, proving the displayed nonlinear <covariant wave equation for the Yang-Mills field strength> on flat spacetime.
// Target: special-relativity.bigb
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