The resolvent of the Nelson Hamiltonian improves positivity

Jonas Lampart (1)

1 ICB - Laboratoire Interdisciplinaire Carnot de Bourgogne

We prove that the resolvent of the renormalised Nelson Hamiltonian at fixed total momentum P improves positivity in the (momentum) Fock-representation, for every P. Our argument is based on an explcit representation of the renormalised operator and its domain using interior boundary conditions.

Mots clés: Nelson model, Energy renormalization, Positivity improving operators

Domaines: Physique mathématique [math-ph]; Analyse fonctionnelle [math.FA]

Jonas Lampart. The resolvent of the Nelson Hamiltonian improves positivity. Mathematical Physics, Analysis and Geometry, 2021, 24 (1), pp.2. ⟨10.1007/s11040-021-09374-6⟩. ⟨hal-02958107v2⟩