 Gauge field strength

The curvature of a non-Abelian gauge field is $F_{\mu \nu }={\partial }_{\mu }{A}_{\nu }-{\partial }_{\nu }{A}_{\mu }+[A_{\mu },A_{\nu }]$. It satisfies $[D_{\mu },D_{\nu }]=F_{\mu \nu }$ and transforms as $F_{\mu \nu }\mapsto g{F}_{\mu \nu }{g}^{-1}$.