Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively

The Nelson model, describing a quantum mechanical particle linearly coupled to a bosonic field, exhibits the infrared problem in the sense that no ground state exists at arbitrary total momentum. However, passing to a non-Fock representation, one can prove the existence of so-called dressed one-particle states. In this article, we give a simple non-perturbative proof for the existence of such one-particle states at arbitrary coupling strength and for almost all total momenta in a physically motivated momentum region. Our results hold both for the non- and the semi-relativistic Nelson model.