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arXiv · 1603.01108

The quantum-to-classical transition: contraction of associative products

A. Ibort·V. I. Man'ko·G. Marmo·A. Simoni·C. Stornaiolo·F. Ventriglia
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Abstract

The quantum-to-classical transition is considered from the point of view of contractions of associative algebras. Various methods and ideas to deal with contractions of associative algebras are discussed that account for a large family of examples. As an instance of them, the commutative algebra of functions in phase space, corresponding to classical physical observables, is obtained as a contraction of the Moyal star-product which characterizes the quantum case. Contractions of associative algebras associated to Lie algebras are discussed, in particular the Weyl-Heisenberg and $SU(2)$ groups are considered.

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A. Ibort, V. I. Man'ko, G. Marmo, A. Simoni, C. Stornaiolo, F. Ventriglia. 2016-03-03. The quantum-to-classical transition: contraction of associative products. https://doi.org/10.1088/0031-8949/91/4/045201

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