We study the quasi-classical limit of a quantum system composed of
finitely many non-relativistic particles coupled to a quantized field
in Nelson or Pauli-Fierz-type models. We prove that, as the field
becomes classical and the corresponding degrees of freedom are traced
out, the effective Hamiltonian of the particles converges in resolvent
sense to a self-adjoint Schroedinger operator with a additional
potentials, either electric and/or magnetic, depending on the state of
the field. In addition, we prove convergence of the ground state
energy of the full system to a suitable effective variational problem
involving the classical state of the field.
Joint work with M. Falconi (Tuebingen) and M. Olivieri (Roma "Sapienza").