Baumgartner, B. Measure theoretic ergodic theory in quantum mechanics. (English) Zbl 0432.46063 Rep. Math. Phys. 15, 391-397 (1979). The measure theoretic ergodic theory is applied to quantum systems. The time evolution is considered as a point transformation in the set of a \( C^{*} \)-algebra. Invariant Borel measures on this set are shown to exist, so there is a measure theoretic dynamic system. Interrelations between this system and the corresponding quantum dynamical system are established. This review text is based on a scanned copy of the printed version. It was converted to LaTeX using MathPix and a specifically developed LLM to assign the text parts to the metadata. It may contain errors, misassignments, or gaps; in particular, the reviewer signature has not yet been extracted reliably in general. If you notice any errors, please report them directly to our editorial team via the Contact Form. Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page MSC: 46L55 Noncommutative dynamical systems 28D10 One-parameter continuous families of measure-preserving transformations Keywords:spectral analysis; measure theoretic ergodic theory; time evolution; invariant Borel measures; measure theoretic dynamic system × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Walters, P., Ergodic theory—Introductory lectures, 1975, Springer: Springer Berlin-Heidelberg-New York · Zbl 0299.28012 [2] Guichardet, A.: Systèmes dynamiques non-commutatifs, CNRS, Series Asterisques 14, Paris. · Zbl 0276.46033 [3] Radin, Ch., Commun. Math. Phys., 21, 291, 1971 · Zbl 0211.43504 [4] Dixmier, Les C^∗-algèbres et leurs représentations, 1969, Gauthier-Villars: Gauthier-Villars Paris · Zbl 0174.18601 [5] Arnold, V. I.; Avez, A., Ergodic problems of classical mechanics, 1968, Benjamin: Benjamin New York–Amsterdam · Zbl 0167.22901 [6] Reed, M.; Simon, B., Methods of modern mathematical physics, II, Fourier analysis, self-adjointness, 1975, Academic Press: Academic Press New York-San Francisco-London · Zbl 0308.47002 [7] Lanford, O. E.; Robinson, D. W., Commun. Math. Phys., 24, 193, 1972 [8] Robinson, D. W.: Dynamics in quantum statistical mechanics, ZiF-preprint, Universität Bielefeld. [9] Kastler, D.; Mebkhout, M.; Loupias, G.; Michael, L., Commun. Math. Phys., 27, 195, 1972 · Zbl 0239.46069 [10] Radin, Ch.: Pointwise ergodic theory and operator algebras, preprint. · Zbl 0418.46055 [11] Bargmann, V., Ann. Math., 59, 1, 1954 · Zbl 0055.10304 [12] Lukacs, E., Characteristic functions, 1970, Griffin: Griffin London · Zbl 0201.20404 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.