SU(2) Yang-Mills Coulomb Green's functions in the presence of a generalized Wu-Yang configuration

The Coulomb propagator in a generalized Wu-Yang configuration $A$ is considered and its dependence on zero modes is investigated. It is found that for (i) $A$ equal to a pure Wu-Yang monopole there are no zero modes and (ii) $A$ equal to a pure gauge one zero mode appears. Pure-gauge boundary conditions at the origin lead to an ambiguity which must be resolved by introducing a new parameter $\theta$ ($0<\mathrm{}\theta <\pi$). For those cases without zero modes an exact multipole expansion is constructed.