Renormalization of spin$\text{unicode}x2013$boson interactions mediated by singular form factors

We study and discuss the extension of the rotating-wave spin$\text{unicode}x2013$boson model, together with more general models describing a system$\text{unicode}x2013$field coupling with a similar rotating-wave structure, to interactions mediated by possibly singular (non-normalizable) form factors satisfying a weaker growth constraint. To this purpose, a construction of annihilation and creation operators as continuous maps on a scale of Fock spaces, together with a rigorous renormalization procedure, is employed.