Semiclassical Scattering in Yang-Mills Theory

Abstract

A classical solution to the Yang-Mills theory is given a new semiclassical interpretation. The boundary value problem on a complex time contour which arises from the semiclassical approximation to multiparticle scattering amplitudes is reviewed and applied to the case of Yang- Mills theory. The solution describes a classically for- bidden transition between states with a large average number of particles in the limit $g\rightarrow 0$. It dominates a transition probability with a semiclassical suppression factor equal to twice the action of the well- known BPST instanton. Hence, it is relevant to the pro- blem of high energy tunnelling. It describes transitions of unit topological charge for an appropriate time contour. Therefore, it may have a direct interpretation in terms of fermion number violating processes in electroweak theory. The solution describes a transition between an initial state with parametrically fewer particles than the final state. Thus, it may be relevant to the study of semiclassical initial state corrections in the limit of a small number of initial particles. The implications of these results for multiparticle production in electroweak theory are also discussed.