Mapping of a thin-film ferromagnet to electrodynamics

We consider a field-theoretic description of a thin-film ferromagnet with easy-plane anisotropy. An extension of the well-known duality with electrostatics in 2-dimensional space to (2+1)-dimensional spacetime maps this system to a theory of electrodynamics. The low-energy description is the familiar Maxwell electrodynamics. Spin waves become electromagnetic waves, whereas vortices turn into particles whose electric charge equals the vortex number. Vortices have no inertia but experience a Lorentz-like force due to a background magnetic field whose strength is equal to spin density. This mapping allows us to calculate the emission of spin waves by rotating vortices using the direct analogy with the emission of electromagnetic waves by a rotating electric dipole.