Yang–Mills fields with external source

A procedure for quantizing a non-Abelian gauge theory with Lagrangian
$$L=-\frac 14 F_{\mu \nu }^a F_a^{\mu \nu }+J_a^\mu V_\mu ^a$$
near a nontrivial classical solution is considered. The theories are classified with respect to the external current. The gluon propagator in a model spherically symmetric non-Abelian field is constructed and investigated.