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)

BibTexBibNote ® (generic)BibNote ® (RIS)

MedlineRefWorks

PT Journal Article
TI Groups and probabilities at the foundations of quantum mechanics
AU Smorodinskii Ya A
FAU Smorodinskii YA
AU Shelepin A L
FAU Shelepin AL
AU Shelepin L A
FAU Shelepin LA
DP 10 Dec, 1992
TA Phys. Usp.
VI 35
IP 12
PG 1005-1051
RX 10.1070/PU1992v035n12ABEH002281
URL https://ufn.ru/en/articles/1992/12/a/
SO Phys. Usp. 1992 Dec 10;35(12):1005-1051

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