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PreprintarXiv licencearXiv

Holomorphy of the ground state and energy for bosonic quadratic Hamiltonians

  • Kota Imura
  • Shinnosuke Izumi
  • Yasumichi Matsuzawa
  • Itaru Sasaki
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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.

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Cite

BibTeXRIS
BibTeX
@misc{imura2026holomorphy,
  title = {{Holomorphy of the ground state and energy for bosonic quadratic Hamiltonians}},
  author = {Kota Imura and Shinnosuke Izumi and Yasumichi Matsuzawa and Itaru Sasaki},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.27862},
  eprint = {2608.27862},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.27862},
}
RIS
TY  - UNPB
TI  - Holomorphy of the ground state and energy for bosonic quadratic Hamiltonians
AU  - Kota Imura
AU  - Shinnosuke Izumi
AU  - Yasumichi Matsuzawa
AU  - Itaru Sasaki
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.27862
UR  - https://arxiv.org/abs/2608.27862
AB  - 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.
ER  -