Dirac magnetic poles forbidden in s-matrix theory

The residue of the one-photon exchange pole in the amplitude for the scattering of massive particles is calculated, using only generalized unitarity and the correspondence of particles to representations of the proper inhomogeneous Lorentz group. It is found that magnetic monopole coupling results in a residue which contains square-root singularities. Such a nonanalytic term is incompatible with the analyticity assumptions of S-matrix theory, and if it were present, the photon would appear in the annihilation channel as an intermediate state in all partial waves instead of only one. This behavior is theoretically implausible and discourages further experimental search for magnetic monopoles.