发表机构
Russian Quantum Center; Moscow Institute of Physics and Technology; Vereshchagin Institute for High Pressure Physics of the Russian Academy of Sciences; National Research Center “Kurchatov Institute”; P. N. Lebedev Physical Institute of the Russian Academy of Sciences（俄罗斯量子中心; 莫斯科物理技术学院; 俄罗斯科学院韦列夏金高压物理研究所; 库尔恰托夫国家研究中心; 俄罗斯科学院P.N.列别捷夫物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文基于$f$-形变振子形式提出统一代数方法，将单模与双模自旋-玻色子映射（如Holstein-Primakoff、Dyson-Maleev及Jordan-Schwinger变换）解释为共同结构的分解，并导出新的精确玻色子表示。
AI 中文摘要
我们基于$f$-形变振子形式发展了一种统一的自旋-玻色子变换代数方法。在单模情形下，我们证明Holstein-Primakoff和Dyson-Maleev变换以及插值$\alpha$-族，是同一代数确定对象的不同分解。因此，标准自旋-玻色子映射可被解释为一种共同结构的实现，这使得在物理子空间上精确的代数内容与非厄米性、度规选择以及物理子空间之外的扩展相关效应得以清晰分离。在双模情形下，同一方法既产生了Jordan-Schwinger变换的形变版本，也产生了新的精确双模实现。我们的结果为已知的自旋-玻色子变换提供了统一描述，并自然地导出了新的玻色子表示。
英文摘要
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.
Comments21 pages, 1 figure. Corrected an author's name; minor corrections
