Kinematics of Yang-Mills solitons

In SU(2) Yang-Mills theory, theN-monopole configuration space is a bundle with fibers isomorphic to U(1)×...×U(1), and state vectors for which each monopole has chargen e/2 are homogeneous of degreen with respect to each U(1). Translations and rotations are defined for individual monopoles in theN-monopole space. The commutator of two translations is found to be a U(1) transformation that agrees for large monopole separation with the analogous phase change accompanying the translation of a charged point particle in an external magnetic field. The theory developed here is applied in a companion paper to prove a spin-statistics theorem for monopoles in SU(2) Yang-Mills theory.