  We study a class of quantum Hamiltonian models describing a family of $N$
two-level systems (spins) coupled with a structured boson field of positive
mass, with a rotating-wave coupling mediated by form factors possibly
exhibiting ultraviolet divergences (hence, non-normalizable). Spin-spin
interactions which do not modify the total number of excitations are also
included. Generalizing previous results in the single-spin case, we provide
explicit expressions for the self-adjointness domain and the resolvent operator
of such models, both of them carrying an intricate dependence on both the
spin-field and spin-spin coupling via a family of concatenated propagators.
This construction is also shown to be stable, in the norm resolvent sense,
under approximations of the form factors via normalizable ones, for example an
ultraviolet cutoff.
