Semiclassical analysis of quantum asymptotic fields in the Yukawa theory

In this article, we study the asymptotic fields of the Yukawa particle-field model of quantum physics in the semiclassical regime h -> 0, with an interaction subject to an ultraviolet cutoff. We show that the tran-sition amplitudes between final (respectively initial) states converge towards explicit quantities involving the outgoing (respectively incoming) wave operators of the nonlinear Schrodinger-Klein-Gordon (S-KG) equation. Thus, we rigorously link the scattering theory of the Yukawa model to that of the Schrodinger- Klein-Gordon equation. Moreover, we prove that the asymptotic vacuum states of the Yukawa model have a phase space concentration property around classical radiationless solutions. Under further assumptions, we show that the S-KG energy admits a unique minimizer modulo symmetries and we identify exactly the semiclassical measure of Yukawa ground states. Some additional consequences of asymptotic completeness are also discussed, and some further open questions are raised.