PERIODIC INSTANTONS AND SCATTERING-AMPLITUDES

We discuss the role of periodic euclidean solutions with two turning points and zero winding number (periodic instantons) in instanton-induced processes below the sphaleron energy E(sph). We find that the periodic instantons describe certain multiparticle scattering events leading to the transitions between topologically distinct vacua. Both the semiclassical amplitudes and inital and final states of these transitions are determined by the periodic instantons. Furthermore, the corresponding probabilities are maximal among all states of a given energy. We show that at E << E(sph), the periodic instantons can be approximated by infinite chains of ordinary instantons and anti-instantons, and they naturally emerge as deformations of the zero-energy instanton. In the framework of the two-dimensional abelian Higgs model and four-dimensional electroweak theory we show, however, that there is no obvious relation between periodic instantons and two-particle scattering amplitudes.