The Casimir energy of skyrmions in the 2+1-dimensional O(3)-model

Abstract

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 and n=2. 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>2 are already classically unstable against decay. The quantum corrections destabilize the classically bound n=2 configuration. Approximate independence of the results with respect to changes in the renormalization scale is demonstrated.