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.

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

References in corpus (9)

• On Nelson-type Hamiltonians and abstract boundary conditions
• On the domain of the Nelson Hamiltonian
• Avoiding Ultraviolet Divergence by Means of Interior-Boundary Conditions
• Hamiltonians Without Ultraviolet Divergence for Quantum Field Theories
• The Renormalised Bogoliubov-Fröhlich Hamiltonian
• A nonrelativistic quantum field theory with point interactions in three dimensions
• Feynman-Kac formulas for the ultra-violet renormalized Nelson model
• On a Direct Description of Pseudorelativistic Nelson Hamiltonians
• On the self-adjointness of H+A*+A

Cited by in corpus (4)

• Ground states and associated path measures in the renormalized Nelson model
• On the global minimum of the energy-momentum relation for the polaron
• A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate
• Feynman-Kac formula and asymptotic behavior of the minimal energy for the relativistic Nelson model in two spatial dimensions