This article is cited in 10 papers

REVIEWS OF TOPICAL PROBLEMS

Groups and probabilities at the foundations of quantum mechanics

Ya. A. Smorodinskii^a, A. L. Shelepin^b, L. A. Shelepin<sup>c

a</sup> Russian Research Centre "Kurchatov Institute", Moscow
^b Moscow Institute of Radio-Engineering, Electronics and Automation
^c P. N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow

Abstract: 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

Received: June 17, 1992

DOI: 10.3367/UFNr.0162.199212a.0001

 English version: Physics–Uspekhi, 1992, 35:12, 1005–1051