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Peer-reviewedCC BY 4.0Annales Henri Poincaré

Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions

  • Benjamin Hinrichs1
  • Jonas Lampart2
  • Javier Valentín Martín1
  1. 1Institut für Mathematik, Institut für Photonische Quantensysteme, Universität Paderborn, Warburger Str. 100, 33098, Paderborn, Germany
  2. 2Universite Bourgogne Europe,CNRS, Laboratoire Interdisciplinaire Carnot de Bourgogne, ICB UMR 6303, 21000, Dijon, France
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Abstract

We study the ultraviolet problem for models of a small quantum mechanical system with bounded Hamiltonian linearly coupled to a bosonic quantum field. In the main examples the small system is finite dimensional, such as in the (many-)spin boson model or its rotating-wave approximation. If the state change of the system upon emission or absorption of a boson is given by a bounded and normal or 2-nilpotent operator, which is the case for the previously named examples, we prove an optimal renormalization result. In particular, we prove the norm resolvent convergence of appropriately regularized models to the renormalized one. Our method consists of a dressing transformation argument in the normal case and an appropriate interior boundary condition for the 2-nilpotent case.

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Cite

BibTeXRIS
BibTeX
@article{hinrichs2026ultraviolet,
  title = {{Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions}},
  author = {Benjamin Hinrichs and Jonas Lampart and Javier Valentín Martín},
  journal = {Annales Henri Poincaré},
  year = {2026},
  month = jun,
  doi = {10.1007/s00023-026-01724-w},
  eprint = {2502.04876},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05189857v2},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions
AU  - Benjamin Hinrichs
AU  - Jonas Lampart
AU  - Javier Valentín Martín
PY  - 2026
DA  - 2026/06/30
JO  - Annales Henri Poincaré
DO  - 10.1007/s00023-026-01724-w
UR  - https://hal.science/hal-05189857v2
AB  - We study the ultraviolet problem for models of a small quantum mechanical system with bounded Hamiltonian linearly coupled to a bosonic quantum field. In the main examples the small system is finite dimensional, such as in the (many-)spin boson model or its rotating-wave approximation. If the state change of the system upon emission or absorption of a boson is given by a bounded and normal or 2-nilpotent operator, which is the case for the previously named examples, we prove an optimal renormalization result. In particular, we prove the norm resolvent convergence of appropriately regularized models to the renormalized one. Our method consists of a dressing transformation argument in the normal case and an appropriate interior boundary condition for the 2-nilpotent case.
SN  - 1424-0637
SN  - 1424-0661
ER  -