The Nelson model describes a system of quantum mechanical particles
linearly coupled to a scalar bose field, which was introduced by E.
Nelson. The bottom of the spectrum of the Hamiltonian is called the
ground state energy. If the ground state energy is an eigenvalue, the
eigenvector associated with this is called a ground state. The existence
of a ground state of the massless Nelson Hamiltonian with a singular
perturbation is considered. Since the ground state energy of the
decoupled Hamiltonian is an embedded eigenvalue, the existence of a
ground state for the Nelson Hamiltonian is not trivial.
