  We study the quasi-classical limit of the Pauli-Fierz model: the system is
composed of finitely many non-relativistic charged particles interacting with a
bosonic radiation field. We trace out the degrees of freedom of the field, and
consider the classical limit of the latter. We prove that the partial trace of
the full Hamiltonian converges, in resolvent sense, to an effective
Schr\"odinger operator with magnetic field and a corrective electric potential
that depends on the field configuration. Furthermore, we prove the convergence
of the ground state energy of the microscopic system to the infimum over all
possible classical field configurations of the ground state energy of the
effective Schr\"odinger operator.
