Asymptotic states for kink–meson scattering

Abstract

The definition of a quantum state corresponding to a wave packet far from a global soliton is considered. We define an asymptotic quantum state corresponding to a localized wave packet of elementary quanta far from a kink. We demand that the state satisfies two properties. First, it must evolve in time via a rigid translation of the wave packet, up to the usual wave packet spreading and corrections which are exponentially suppressed in the distance to the kink. Second, the state must be invariant under a simultaneous translation of the kink and the wave packet. We explicitly construct the leading quantum corrections to an asymptotic state consisting of a meson approaching a kink. We expect this construction to readily generalize to elementary quanta in the presence of any global soliton.