Quasi-classical ground states. I. linearly coupled Pauli-Fierz hamiltonians

We consider a spinless, non-relativistic particle bound by an external potential and linearly coupled to a quantized radiation field. The energy E(u, f) of product states of the form u ⊗ Ψ f , where u is a normalized state for the particle and Ψ f is a coherent state in Fock space for the field, gives the energy of a Klein-Gordon-Schrödinger system. We minimize the functional E(u, f) on its natural energy space. We prove the existence and uniqueness of a ground state under general conditions on the coupling function. In particular, neither an ultraviolet cutoff nor an infrared cutoff are imposed