Bohr's correspondence principle for the renormalized Nelson model

Zied Ammari (1) , Marco Falconi (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 UZH - Universität Zürich [Zürich] = University of Zurich

In the mid Sixties Edward Nelson proved the existence of a consistent quantum field theory that describes the Yukawa-like interaction of a non-relativistic nucleon field with a relativis-tic meson field. Since then it is thought, despite the renormalization procedure involved in the construction, that the quantum dynamics should be governed in the classical limit by a Schrödinger-Klein-Gordon system with Yukawa coupling. In the present paper we prove this fact in the form of a Bohr correspondence principle.

Mots clés: Nelson model; Schrödinger-Klein-Gordon system; Yukawa interaction; Classical limit

Domaines: Equations aux dérivées partielles [math.AP]

Zied Ammari, Marco Falconi. Bohr's correspondence principle for the renormalized Nelson model. SIAM Journal on Mathematical Analysis, 2017, 49 (6), pp.5031-5095. ⟨10.1137/17M1117598⟩. ⟨hal-01687438⟩