Valleys in Minkowski space and instanton-induced cross sections

We generalize the valley method for the calculation of instanton-induced cross sections, and reformulate it directly in the Minkowski space using the Keldysh diagram technique. The summation over all finite states is made implicit without our approach, and the fields of outgoing W-bosons are effectively taken into account by a classical field with specific analytic properties, which we call the 'alien' field. (orig.)