  We consider Dirichlet realizations of Pauli-Fierz type operators generating
the dynamics of non-relativistic matter particles which are confined to an
arbitrary open subset of the Euclidean position space and coupled to quantized
radiation fields. We find sufficient conditions under which their domains and a
natural class of operator cores are determined by the domains and operator
cores of the corresponding Dirichlet-Schr\"{o}dinger operators and the
radiation field energy. Our results also extend previous ones dealing with the
entire Euclidean space, since the involved electrostatic potentials might be
unbounded at infinity with local singularities that can only be controlled in a
quadratic form sense, and since locally square-integrable classical vector
potentials are covered as well. We further discuss Neumann realizations of
Pauli-Fierz type operators on Lipschitz domains.
