One-loop quantum corrections to the classical vortices in (2+1)-dimensional O(3) models are evaluated. Skyrme and Zeeman potential terms are used to stabilize the size of topological solitons. Contributions from zero modes, bound states and scattering phase shifts are calculated for vortices with winding index $n=1\mathrm{}$ and $n=2.\mathrm{}$ For both cases the S matrix shows a pronounced series of resonances for magnon-vortex scattering in analogy to the well-established baryon resonances in hadron physics, while vortices with $n>\mathrm{}2\mathrm{}$ are already classically unstable against decay. The quantum corrections destabilize the classically bound $n=2\mathrm{}$ configuration. Approximate independence of the results with respect to changes in the renormalization scale is demonstrated.

• Received 26 July 1999

DOI:https://doi.org/10.1103/PhysRevB.61.2819