  We study the interactions of non-abelian vortices in two spatial dimensions.
These interactions have novel features, because the Aharonov-Bohm effect
enables a pair of vortices to exchange quantum numbers. The cross section for
vortex-vortex scattering is typically a multi-valued function of the scattering
angle. There can be an exchange contribution to the vortex-vortex scattering
amplitude that adds coherently with the direct amplitude, even if the two
vortices have distinct quantum numbers. Thus two vortices can be
``indistinguishable'' even though they are not the same.
