What we think about multi-particle amplitudes

Certain classical solutions which serve as generating functions of tree multi-particle amplitudes are constructed in the Kähler sigma model. The one-loop contribution to the multi-particle amplitudes is computed as a functional determinant in the background of such a classical field. Topologically nontrivial solutions, that is generating functions of the instanton mediated multi-particle amplitudes, are constructed as well. An example of this type is also given for the $SU(2)$ Yang-Mills theory