  We consider interaction of a probe monopole-antimonopole pair in the vacuum
of the Abelian Higgs model. For simplicity, the mass of the Higgs particle is
assumed to be much larger than the mass of the photon (London limit). In case
of a massive photon the straightforward application of the Zwanziger formalism
to accommodate both magnetic and electric charges is known to result in gauge
dependence and infrared instabilities. We argue that the use of the string
representation of the Abelian Higgs model allows to ameliorate both
difficulties. In particular, we arrive at a well defined expression for the
potential energy of the static monopole sources. We argue that the
monopole-antimonopole interaction cannot be described by a massive photon
exchange with a definite propagator having simple analytical properties.
