  We construct the Faddeev-Kulish dressed multiparticle states of electrically
and magnetically charged particles, incorporating the effects of real and
virtual soft photons. We calculate the properties of such dressed states under
Lorentz transformations, and find that they can be identified with the pairwise
multi-particle states that transform under the pairwise little group. The
shifts in the dressing factors under Lorentz transformations are finite and
have a simple geometric interpretation. Using the transformation properties of
the dressed states we also present a novel, fully quantum field theoretic
derivation of the geometric (Berry) phase obtained by an adiabatic rotation of
the Dirac string, and also of the Dirac quantization condition. For half
integer pairwise helcity, we show that these multiparticle states have flipped
spin-statistics, reproducing the surprising fact that fermions can be made out
of bosons.
