A Feynman-Kac Formula for the Subcritical Ultraviolet-Renormalized Spin Boson Model

We prove a Feynman-Kac formula (FKF) for the self-energy renormalized spin boson Hamiltonian, describing a two-state quantum system linearly coupled to a bosonic quantum field. Similar to recent FKFs for the Fr\"ohlich polaron and the non- and semi-relativistic Nelson models, it yields a probabilistic treatment of the spin as a jump process, but treats the field on the usual bosonic Fock space. As an application, we prove that the existence of ground states for infrared-regular models persists the removal of an ultraviolet cutoff.