  Generalized spin-boson (GSB) models describe the interaction between a
quantum mechanical system and a structured boson environment, mediated by a
family of coupling functions known as form factors. We propose an extension of
the class of GSB models which can accommodate non-normalizable form factors,
provided that they satisfy a weaker growth constraint, thus accounting for a
rigorous description of a wider range of physical scenarios; we also show that
such "singular" GSB models can be rigorously approximated by GSB models with
normalizable form factors. Furthermore, we discuss in greater detail the
structure of the spin-boson model with a rotating wave approximation (RWA): for
this model, the result is improved via a nonperturbative approach which enables
us to further extend the class of admissible form factors, as well as to
compute its resolvent and characterize its self-adjointness domain.
