Non-Trivial Renormalization of Spin-Boson Models with Supercritical Form Factors

In this paper we construct the non-trivial, renormalized Hamiltonian for a class of spin-boson models with supercritical form factors, including the one describing the Weisskopf-Wigner spontaneous emission. The renormalization is performed through both a self-energy and mass renormalization, in the so-called Hamiltonian formalism of constructive quantum field theory, implemented by a non-unitary dressing transformation. This solves the problem of triviality for unitarily-renormalized supercritical spin-boson models.