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arXiv · 2605.11725

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

Daniel M. Fröhlich·Benjamin Hinrichs
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Abstract

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.

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Daniel M. Fröhlich, Benjamin Hinrichs. 2026-05-12. A Feynman-Kac Formula for the Subcritical Ultraviolet-Renormalized Spin Boson Model. https://arxiv.org/abs/2605.11725

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