Existence of a ground state for the Nelson model with a singular perturbation

TL;DR

This paper proves the existence of a ground state for the Nelson Hamiltonian with a singular perturbation, establishing self-adjointness and ground state existence for all coupling constants.

Contribution

It demonstrates the ground state existence and self-adjointness of the Nelson Hamiltonian with a singular perturbation for any coupling strength.

Findings

Ground state exists for all coupling constants.

Hamiltonian is self-adjoint.

Results apply to singular perturbations.

Abstract

The existence of a ground state of the Nelson Hamiltonian with a perturbation is considered. The self-adjointness of the Hamiltonian and the existence of a ground state are proven for arbitrary values of coupling constants.