We investigate a generalized nonlinear O(3) model in three space dimensions where the fields are maps from R 3 ഫ͕ϱ͖ to S 2 . Such maps are classified by a homotopy invariant called the Hopf number which takes integer values. The model exhibits soliton solutions of closed vortex type which have a lower topological bound on their energies. We numerically compute the fields for topological charge 1 and 2 and discuss their shapes and binding energies. The effect of an additional potential term is considered and an approximation is given for the spectrum of slowly rotating solitons. ͓S0556-2821͑97͒00520-1͔

A gauged (2+1)-dimensional version of the Skyrme model is investigated. The gauge group is U (1) and the dynamics of the associated gauge potential is governed by a Maxwell term. In this model there are topologically stable soliton solutions carrying magnetic flux which is not topologically quantized. The properties of rotationally symmetric solitons of degree one and two are discussed in detail. It is shown that the electric field for such solutions is necessarily zero. The solitons' shape, mass and magnetic flux depend on the U (1) coupling constant, and this dependence is studied numerically from very weak to very strong coupling. PACS number(s): 11.10.Kk, 11.10.Lm, 11.27.+d, 12.39.Dc I IntroductionThe Skyrme model is a generalized non-linear sigma model in (3+1) dimensions [1]. It has soliton solutions which, after suitable quantization, are models for physical nucleons [2]. The theory is invariant under the group SO(3) iso of iso-rotations, and electromagnetism is introduced into the model by gauging a U(1) subgroup of SO(3) iso , see [3] for details. The resulting fully coupled Skyrme-Maxwell system is mathematically hard to analyze, but of considerable physical interest: it is here that one should compute the Skyrme model's 1

We present a classical, gauged O(3) -model with an Abelian Chern-Simons term. It shows topologically stable, anyonic vortices as solutions. The fields are studied in the case of rotational symmetry and analytic approximations are found for their asymptotic behaviour. The static Euler-Lagrange equations are solved numerically, where particular attention is paid to the dependence of the vortex' properties on the coupling to the gauge field. We compute the vortex mass and charge as a function of this coupling and obtain bound states for twovortices as well as two-vortices with masses above the stability threshold.