The resolvent of the Nelson Hamiltonian improves positivity

TL;DR

This paper demonstrates that the resolvent of the renormalised Nelson Hamiltonian enhances positivity in the momentum Fock-representation for all fixed total momenta, using explicit operator representations and interior boundary conditions.

Contribution

It introduces an explicit representation of the renormalised Nelson Hamiltonian's resolvent and its domain, showing positivity improvement across all momenta.

Findings

Resolvant improves positivity in Fock space

Explicit operator representation developed

Positivity enhancement holds for all fixed momenta

Abstract

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.