Complex Time Solutions with Nontrivial Topology and Multi Particle Scattering in Yang-Mills Theory

Abstract

A classical solution to the Yang-Mills theory is given a new semiclassical interpretation in terms of particle scattering. It solves the complex time boundary value problem, which arises in the semiclassical approximation to a multi particle transition probability in the one-instanton sector at fixed energy. The imaginary part of the action of the solution on the complex time contour and its topological charge obey the same relation as the self-dual Euclidean configurations. Hence the solution is relevant for the problem of tunneling with fermion number violation in the electroweak theory. It describes transitions from an initial state with a smaller number of particles to a final state with a larger number of particles. The implications of these results for multi particle production in the electroweak theory are also discussed.