I have seen distinct definitions of gauge covariant derivative (in Yang-Mills theory)
$$ D_\mu \phi = (\partial_\mu + igA_\mu) \phi $$
vs
$$ D_\mu \phi = \partial_\mu \phi + ig[A_\mu,\phi] .$$
I guess the first is the common definition, which is the same as the covariant derivative in QED. What is about the second?
As AccidentalFourierTransform points out, the second expression is the non-abelian generalization of the former. The first one is only valid for the abelian case (QED), while in general Yang Mills the fields are matrices transforming in some representation of the gauge group and the correct form is the latter.
