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.
The quantum-to-classical transition: Contraction of associative products / Ibort, A.; Man'Ko, Vladimir; Marmo, Giuseppe; Simoni, Alberto; Stornaiolo, C.; Ventriglia, Franco. - In: PHYSICA SCRIPTA. - ISSN 0031-8949. - 91:4(2016), p. 045201. [10.1088/0031-8949/91/4/045201]
The quantum-to-classical transition: Contraction of associative products
MAN'KO, VLADIMIR;MARMO, GIUSEPPE;SIMONI, ALBERTO;VENTRIGLIA, FRANCO
2016
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.File | Dimensione | Formato | |
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