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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 1, Pages 181–194 (Mi izv1476)  

This article is cited in 7 scientific papers (total in 7 papers)

On a generalization of canonical quantization

A. S. Kholevo

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: A study is made of Mackey's generalized quantization based on the concept of an imprimitivity system. Let $G$ be a topological group (symmetry group) acting continuously on a transitive $G$-space $X$ (the configuration space of a classical system). The structure of generalized imprimitivity systems is investigated in two cases: for a compact $G$ and for $G=X$ a locally compact type I group (for separable $G$ and Hilbert space $\mathscr H$ in which $G$ has a continuous unitary representation).
Bibliography: 23 titles.

Full text: PDF file (1830 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:1, 175–188

Bibliographic databases:

UDC: 517.986
MSC: Primary 81D07; Secondary 22D30
Received: 18.01.1984

Citation: A. S. Kholevo, “On a generalization of canonical quantization”, Izv. Akad. Nauk SSSR Ser. Mat., 50:1 (1986), 181–194; Math. USSR-Izv., 28:1 (1987), 175–188

Citation in format AMSBIB
\Bibitem{Hol86}
\by A.~S.~Kholevo
\paper On a~generalization of canonical quantization
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 1
\pages 181--194
\mathnet{http://mi.mathnet.ru/izv1476}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=835571}
\zmath{https://zbmath.org/?q=an:0613.22012|0606.22015}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 1
\pages 175--188
\crossref{https://doi.org/10.1070/IM1987v028n01ABEH000872}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Holevo A., “Radon-Nikodym Derivatives of Quantum Instruments”, J. Math. Phys., 39:3 (1998), 1373–1387  crossref  mathscinet  zmath  adsnasa  isi
    2. Gianni Cassinelli, Ernsesto De Vito, Pekka Lahti, Juha-Pekka Pellonpää, “Covariant localizations in the torus and the phase observables”, J Math Phys (N Y ), 43:2 (2002), 693  crossref  mathscinet  zmath
    3. G. Cassinelli, E. De Vito, A. Toigo, “Positive operator valued measures covariant with respect to an Abelian group”, J Math Phys (N Y ), 45:1 (2004), 418  crossref  mathscinet  zmath  adsnasa  isi
    4. Claudio Carmeli, Teiko Heinosaari, Juha-Pekka Pellonpää, Alessandro Toigo, “Extremal covariant positive operator valued measures: The case of a compact symmetry group”, J Math Phys (N Y ), 49:6 (2008), 063504  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Alexander S. Holevo, Juha-Pekka Pellonpää, “Extreme Covariant Observables for Type I Symmetry Groups”, Found Phys, 2009  crossref  isi
    6. Juha-Pekka Pellonpää, “Extreme phase and rotated quadrature measurements”, Phys Scr, t140 (2010), 014032  crossref
    7. Erkka Theodor Haapasalo, Juha-Pekka Pellonpää, “Extreme covariant quantum observables in the case of an Abelian symmetry group and a transitive value space”, J. Math. Phys, 52:12 (2011), 122102  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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