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 $A$?

This post imported from StackExchange Physics at 2020-11-09 19:27 (UTC), posted by SE-user annie marie heart