Renormalization of generalized spin-boson models with critical ultraviolet divergences
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908507280769024 |
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| author | Alvarez, Benjamin Lill, Sascha Lonigro, Davide Martín, Javier Valentín |
| author_facet | Alvarez, Benjamin Lill, Sascha Lonigro, Davide Martín, Javier Valentín |
| contents | We provide a rigorous construction of generalized spin--boson models with commuting transition matrices and form factors exhibiting critical ultraviolet (UV) divergences. That is, we cover all divergences where a self-energy renormalization, but no non-Fock representation, is required. Our method is based on a direct definition of the renormalized Hamiltonian on a sufficiently large test domain, followed by a Friedrichs extension. We then prove that this Hamiltonian coincides with the one obtained by cut-off renormalization. Furthermore, we show that for specific supercritical cases, i.e., when a non-Fock representation is required, the renormalized Hamiltonian is trivial. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_00803 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Renormalization of generalized spin-boson models with critical ultraviolet divergences Alvarez, Benjamin Lill, Sascha Lonigro, Davide Martín, Javier Valentín Mathematical Physics Functional Analysis Operator Algebras 46N50, 47A10, 47B25, 81Q10, 81T16 We provide a rigorous construction of generalized spin--boson models with commuting transition matrices and form factors exhibiting critical ultraviolet (UV) divergences. That is, we cover all divergences where a self-energy renormalization, but no non-Fock representation, is required. Our method is based on a direct definition of the renormalized Hamiltonian on a sufficiently large test domain, followed by a Friedrichs extension. We then prove that this Hamiltonian coincides with the one obtained by cut-off renormalization. Furthermore, we show that for specific supercritical cases, i.e., when a non-Fock representation is required, the renormalized Hamiltonian is trivial. |
| title | Renormalization of generalized spin-boson models with critical ultraviolet divergences |
| topic | Mathematical Physics Functional Analysis Operator Algebras 46N50, 47A10, 47B25, 81Q10, 81T16 |
| url | https://arxiv.org/abs/2508.00803 |