A Feynman-Kac Formula for the Subcritical Ultraviolet-Renormalized Spin Boson Model
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914557562191872 |
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| author | Fröhlich, Daniel M. Hinrichs, Benjamin |
| author_facet | Fröhlich, Daniel M. Hinrichs, Benjamin |
| contents | 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 Fröhlich 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_11725 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Feynman-Kac Formula for the Subcritical Ultraviolet-Renormalized Spin Boson Model Fröhlich, Daniel M. Hinrichs, Benjamin Mathematical Physics 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 Fröhlich 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. |
| title | A Feynman-Kac Formula for the Subcritical Ultraviolet-Renormalized Spin Boson Model |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2605.11725 |