  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.
