The resolvent of the Nelson Hamiltonian improves positivity

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.

Some polishing and minor corrections, in particular to the proof of Lemma A.1 c)