# What tree-level Feynman diagrams are added to QED if magnetic monopoles exist?

Are the added diagrams the same as for the $e-\gamma$ interaction, but with "$e$" replaced by "monopole"? If so, is the force between two magnetic monopoles described by the same virtual $\gamma$-exchange diagrams? I'm anticipating that the answer is 'no', because otherwise I don't see how one could tell magnetic monopoles and electrons apart (besides their mass and coupling strength to the photon). Obviously magnetic monopoles behave differently from electrons when placed in an $E$ or $B$ field.

• This is a very interesting question, but unfortunately, the electron is perturbative precisely when the monopole is not, since the couplings are inverse to each other. So if you do a photon description of the electron perturbation, the monopole perturbation is strong-coupling. This was a subject of several Schwinger papers in the 1960s, although I am not sure what the conclusion is. – Ron Maimon Jun 19 '12 at 21:04

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.