Renormalization of Spin–Boson Interactions Mediated by Singular Form Factors

Abstract. We study and discuss the extension of the rotating-wave spin–boson model, together with more general models describing a system–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.