Title: Symbol correspondences for spin systems Show Chinese title

Title: 自旋系统的符号对应关系

Abstract: The present monograph explores the correspondence between quantum and classical mechanics in the particular context of spin systems, that is, SU(2)-symmetric mechanical systems. Here, a detailed presentation of quantum spin-j systems, with emphasis on the SO(3)-invariant decomposition of their operator algebras, is followed by an introduction to the Poisson algebra of the classical spin system and a similarly detailed presentation of its SO(3)-invariant decomposition. Subsequently, this monograph proceeds with a detailed and systematic study of general quantum-classical symbol correspondences for spin-j systems and their induced twisted products of functions on the 2-sphere. This original systematic presentation culminates with the study of twisted products in the asymptotic limit of high spin numbers. In the context of spin systems, it shows how classical mechanics may or may not emerge as an asymptotic limit of quantum mechanics. Show Chinese abstract

Abstract: 本专著探讨了自旋系统这一特定背景下量子力学与经典力学之间的对应关系，即SU(2)对称的力学系统。 这里详细介绍了量子自旋-j系统，重点在于其算子代数的SO(3)不变分解，随后引入了经典自旋系统的泊松代数，并对其SO(3)不变分解进行了类似的详细介绍。 随后，本专著系统地研究了自旋-j系统的通用量子-经典符号对应关系及其在2球面上函数上的诱导扭曲乘积。 这种原创的系统性阐述最终集中在高自旋数渐近极限中的扭曲乘积研究上。 在自旋系统的背景下，它展示了经典力学是否可能作为量子力学的渐近极限出现。