In fact, the situation for an abelian $U(1)$ gauge theory—which is the case you asked about—is a bit less clear and less well-defined than the case of a non-abelian gauge theory. Think about the running of the coupling constant, for example.
In a non-abelian theory with a Higgs field, one can have classical solutions which look like monopoles, i.e. they create magnetic flux through a sphere at infinity. Nevertheless, they are perfectly non-singular classical solutions, which almost certainly survive in the quantum theory. In a sense, they are composite, that is they are built out of fundamental fields like the gauge fields and the scalars.
From this, you can conclude that when summing up Feynman diagrams you should not include the monopoles as extra degrees of freedom. Rather, their effect should appear after resuming the entire perturbation series. If you truncate the perturbation series to any finite order, you will not capture the presence of the magnetic monopoles.
This post imported from StackExchange Physics at 2015-04-11 10:21 (UTC), posted by SE-user Sidious Lord