We know the Yang-Mills theory Equation of Motion (eom) without source
$$ * D * F = * (d (* F ) + [A, (* F )])= 0. $$
My question is that what are the most simple form we can boil down this eom to its minimal?
$$ * (d (* (d A + A \wedge A) ) + [A, (* (d A + A \wedge A) )]) $$
$$=* d * d A + * d * (A \wedge A) +A( * (d a + A \wedge A) ) - (* (dA + A \wedge A) ) A=0 $$
This is what I get. How can we massage it further in order to make it as simple as possible but similar to the Maxwell's ---
$$ * d * d A + ... =0? $$ What is the simplest form of $ ...$ term?
p.s. What I got so far is that $ ...$ term is $$C=* d * (A \wedge A) +A( * (d a + A \wedge A) ) - (* (dA + A \wedge A) ) A.$$ Do we have better way to simplify this complicated $C$ in terms of $A$?