Abstract
This chapter presents the basic mathematical framework for quantum mechanics of spin systems. Much of the material can be found in texts in representation theory (some found within the list of references at the beginning of Chap. 2) and quantum theory of angular momentum (e.g. [13, 14, 16, 23, 46, 63, 65], some of these being textbooks in quantum mechanics which can also be used by the reader not too familiar with the subject as a whole). Our emphasis here is to provide a self-contained presentation of quantum spin systems where, in particular, the combinatorial role of Clebsch-Gordan coefficients and various kinds of Wigner symbols is elucidated, leading to the SO(3)-invariant decomposition of the operator product which, strangely enough, we have not found explicitly done anywhere.
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Notes
- 1.
When n 0 is seen as a point on the unit sphere \(S^{2} \subset \mathbb{R}^{3}\), it is also called the “north pole”.
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Rios, P., Straume, E. (2014). Quantum Spin Systems and Their Operator Algebras. In: Symbol Correspondences for Spin Systems. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-08198-4_3
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DOI: https://doi.org/10.1007/978-3-319-08198-4_3
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