Non-Abelian gauge transformation
= Non-Abelian gauge transformation
{title2=$A_\mu\mapsto RA_\mu R^{-1}-g^{-1}(\partial_\mu R)R^{-1}$}
For the convention $D_\mu=\partial_\mu+gA_\mu$, a <gauge group> transformation $\Phi\mapsto R\Phi$ acts on the <gauge potential> by $A_\mu\mapsto RA_\mu R^{-1}-g^{-1}(\partial_\mu R)R^{-1}$. The <gauge field strength> transforms by conjugation. This makes $D_\mu\Phi$ transform in the same <gauge group representation> as $\Phi$.