Transmutation of momentum into position in magnetic vortices

We show that transmutation of linear momentum into position may occur in a system of three magnetic vortices thanks to a direct link between topology and dynamics in a ferromagnet. This happens via exchange between the linear momentum of a vortex-antivortex pair and the position of a single vortex during a semi-elastic scattering process. Vortex polarity switching occurs in the case of inelastic collisions.