SOLITON-LIKE SCATTERING IN THE O(3) SIGMA-MODEL IN (2+1) DIMENSIONS

We consider the instanton solution of the O(3) sigma-model in two Euclidean dimensions as static solitons of the same model in (2 + 1) dimensions, and study their scattering properties. Most of the work involves numerical simulations. We find that in general the solitons scatter at 90-degrees. During the scattering solitons change their size; in most cases they shrink. For head-on collisions when two incoming solitons are of different sizes after the scattering their sizes are equal. Non-zero impact parameter or the initial spin lead to the scattering at different angles. Most of these results are in agreement with the results obtained in the collective coordinate approach. We also look at the scattering of solitons and antisolitons. In this case solitons and antisolitons attract and annihilate each other giving out radiation. The energy of the radiation is strongly peaked and flows at the velocity of light.