Groups and probabilities at the foundations of quantum mechanics

Ya.A. Smorodinskii, A.L. Shelepin, L.A. Shelepin^a
^aLebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation

The current state of the foundations of quantum mechanics is discussed. The analysis takes as its starting point the theory of probability amplitudes, which is intimately related to the group-theoretic approach. A detailed examination is presented of the relationships of classical and quantum theories, the transition to the classical limit, the different forms of uncertainty relations, and the properties of quantum structures determined by the Clebsch--Gordan coefficients. Possible future generalizations are examined, including those involving quantum algebras.

PACS: 03.65.Ta, 03.65.Db, 02.50.Cw (all)
DOI: 10.1070/PU1992v035n12ABEH002281
URL: https://ufn.ru/en/articles/1992/12/a/
Citation: Smorodinskii Ya A, Shelepin A L, Shelepin L A "Groups and probabilities at the foundations of quantum mechanics" Sov. Phys. Usp. 35 (12) 1005–1051 (1992)

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%0 Journal Article
%T Groups and probabilities at the foundations of quantum mechanics
%A Ya. A. Smorodinskii
%A A. L. Shelepin
%A L. A. Shelepin
%I Physics-Uspekhi
%D 1992
%J Phys. Usp.
%V 35
%N 12
%P 1005-1051
%U https://ufn.ru/en/articles/1992/12/a/
%U https://doi.org/10.1070/PU1992v035n12ABEH002281

Оригинал: Смородинский Я А, Шелепин А Л, Шелепин Л А «Групповые и вероятностные основы квантовой теории» УФН 162 (12) 1–95 (1992); DOI: 10.3367/UFNr.0162.199212a.0001