Ground states of a model in nonrelativistic quantum electrodynamics. I

The system of a one charged nonrelativislic particle with external potentials minimally coupled to a massless quantized radiation field is considered. An ultraviolet cutoff is imposed on the quantized radiation field and the charged particle has spin 1/2. The class of external potentials considered in this paper contains Coulomb potentials. It is shown that the ground states of the system exist provided that a coupling constant is in a region.