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PreprintCC BY 4.0arXiv

Spin-Boson Mappings in the Formalism of f-Deformations

  • Vladimir A. Orlov
  • Liubov A. Markovich
  • Andrey V. Mikheyenkov
  • Vladimir I. Man'ko
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Abstract

We develop a unified algebraic approach to spin-boson transformations based on the formalism of f-deformed oscillators. In the single-mode case, we show that the Holstein-Primakoff and Dyson-Maleev transformations, together with the interpolating α-family, arise as different factorizations of the same algebraically determined object. The standard spin-boson mappings can thus be interpreted as realizations of a common structure, which makes it possible to clearly separate the exact algebraic content on the physical subspace from effects associated with non-Hermiticity, the choice of metric, and extensions beyond the physical subspace. In the two-mode case, the same approach yields both deformed versions of the Jordan-Schwinger transformation and new exact two-mode realizations. Our results provide a unified description of known spin-boson transformations and naturally lead to new bosonic representations.

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Cite

BibTeXRIS
BibTeX
@misc{orlov2026spinboson,
  title = {{Spin-Boson Mappings in the Formalism of $f$-Deformations}},
  author = {Vladimir A. Orlov and Liubov A. Markovich and Andrey V. Mikheyenkov and Vladimir I. Man'ko},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22502},
  eprint = {2609.22502},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22502},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Spin-Boson Mappings in the Formalism of f-Deformations
AU  - Vladimir A. Orlov
AU  - Liubov A. Markovich
AU  - Andrey V. Mikheyenkov
AU  - Vladimir I. Man'ko
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.22502
UR  - https://arxiv.org/abs/2609.22502
AB  - We develop a unified algebraic approach to spin-boson transformations based on the formalism of f-deformed oscillators. In the single-mode case, we show that the Holstein-Primakoff and Dyson-Maleev transformations, together with the interpolating α-family, arise as different factorizations of the same algebraically determined object. The standard spin-boson mappings can thus be interpreted as realizations of a common structure, which makes it possible to clearly separate the exact algebraic content on the physical subspace from effects associated with non-Hermiticity, the choice of metric, and extensions beyond the physical subspace. In the two-mode case, the same approach yields both deformed versions of the Jordan-Schwinger transformation and new exact two-mode realizations. Our results provide a unified description of known spin-boson transformations and naturally lead to new bosonic representations.
ER  -