Holomorphy of the ground state and energy for bosonic quadratic Hamiltonians

[2608.27862] Holomorphy of the ground state and energy for bosonic quadratic Hamiltonians Skip to main content Search Submit Donate Log in Mathematical Physics arXiv:2608.27862 (math-ph) [Submitted on 28 Aug 2026] Title: Holomorphy of the ground state and energy for bosonic quadratic Hamiltonians Authors: Kota Imura , Shinnosuke Izumi , Yasumichi Matsuzawa , Itaru Sasaki View PDF HTML (experimental) Abstract: We study the holomorphy of the ground state and its energy with respect to the coupling constant for bosonic quadratic Hamiltonians. We prove general theorems establishing this holomorphy, thereby providing a rigorous justification for formal perturbative expansions. This theory is applied to several concrete models, including the single pair interaction model and the Pauli-Fierz model in the dipole approximation. Importantly, for the Pauli-Fierz model with a realistic ultraviolet cutoff, the perturbation expansions in the elementary charge converge at the physical charge value, even when mass renormalization is taken into account. Furthermore, we explicitly determine the radii of convergence of the ground states and their energies for both the single pair interaction model and the fibers of the translation-invariant Pauli-Fierz model. Comments: 57 pages, 3 figures Subjects: Mathematical Physics (math-ph) MSC classes: 81Q10 (47B25, 81T10, 81V10) Cite as: arXiv:2608.27862 [math-ph] (or arXiv:2608.27862v1 [math-ph] for this version) https://doi.org/10.48550/arXiv.2608.27862 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Itaru Sasaki [ view email ] [v1] Fri, 28 Aug 2026 03:11:52 UTC (52 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math-ph < prev | next > new | recent | 2026-08 Change to browse by: math math.MP References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

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