AN EXAMPLE OF SEMICLASSICAL INSTANTON-LIKE SCATTERING - (1+1)-DIMENSIONAL SIGMA-MODEL

A solution to the classical field equations in the massless (1 + 1)-dimensional O(3) sigma model is found, which describes a multiparticle instanton-like transition at high energy. In the limit of a small number of initial particles, the number of final particles is shown to be also small, and the probability of the transition is suppressed by exp(-2S0), where S0 is the instanton action. This solution, however, does not correspond to the maximum transition probability among all states with given number of incoming particles and energy. Unless the limit g2n(initial) --> 0 is exponentially sensitive to the structure of the initial state, our results imply that well above the sphaleron energy, the instanton-induced cross section becomes again suppressed by the instanton exponent. and the number of final particles is again small.