Semiclassical analysis of quantum asymptotic fields in the Yukawa theory
Abstract
In this article, we study the asymptotic fields of the Yukawa particlefield model of quantum physics, in the semiclassical regime $\hslash\to 0$, with an interaction subject to an ultraviolet cutoff. We show that the transition amplitudes between final (respectively initial) states converge towards explicit quantities involving the outgoing (respectively incoming) wave operators of the nonlinear SchrödingerKleinGordon (SKG) equation. Thus, we rigorously link the scattering theory of the Yukawa model to that of the SchrödingerKleinGordon 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 SKG energy admits a unique minimizer modulo symmetries and 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 DOI:
 10.48550/arXiv.2111.03352
 arXiv:
 arXiv:2111.03352
 Bibcode:
 2021arXiv211103352A
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 81T05;
 81T08;
 81Q20;
 35P25
 EPrint:
 32 pages