Non-Abelian gauge theory action with external currents: gauge invariance?

It is not possible to couple a conventional $c$-number source to a quantized non-abelian gauge field and maintain gauge invariance. For a current $J^\mu=\lambda^a J^\mu_a$, gauge invariance requires covariant current conservation $$ 0= \nabla_\mu J^\mu\equiv \partial_\mu J^\mu + [A_\mu,J^\mu]=0 $$ and this requires a $c$-number(the first term) to equal a term containing an the operator $A_\mu$. It is because of this problem that external sources are introduced into a gauge theory as Wilson Loops $$ W= P\exp\{ i\int A_\mu dx^\mu\} $$ where $P$ denoters a path-ordered integral of the matrix valued ($A_\mu = A_\mu^a \lambda^a$) gauge field.

It is possible to add a kind of classical source to a classical gauge action by using the "Wong equations" in which the internal gauge degrees of freedom in the source are replaced by classical dynamics in a "co-adjoint orbit"