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arXiv · 2609.22502

Spin-Boson Mappings in the Formalism of $f$-Deformations

Vladimir A. Orlov·Liubov A. Markovich·Alexey V. Mikheenkov·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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Vladimir A. Orlov, Liubov A. Markovich, Alexey V. Mikheenkov, Vladimir I. Man'ko. 2026-09-18. Spin-Boson Mappings in the Formalism of $f$-Deformations. https://arxiv.org/abs/2609.22502

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