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TMF, 1984, Volume 59, Number 1, Pages 28–48 (Mi tmf4703)  

This article is cited in 3 scientific papers (total in 3 papers)

Algebras of unbounded operators and vacuum superselection rules in quantum field theory. I. Some properties of Op*-algebras and vector states on them

A. V. Voronin, V. N. Sushko, S. S. Horuzhy


Abstract: In connection with the physical problem of describing vacuum superselection rules in quantum field theory, a study is made of some properties of Op* algebras, namely, the structure of their commutants and invariant and reducing subspaces and vector states on such algebras. For this, a formalism is developed that uses intertwining operators of Hermitian representations of a * algebra. The formalism is used to obtain a number of new properties of the commutants of Op* algebras, and a description is given of classes of subspaces the projection operators onto which lie in the strong or weak commutant. A study is made of the correspondence between vector states on the Op* algebra $\mathscr P$ and on its associated yon Neumann algebra $R=({\mathscr P_w}^{'})^{'}$; generalizations are found of the class of self-adjoint Op* algebras for which a detailed investigation of vector states can be made. Classes of weakly regular, strongly regular, and completely regular vectors for which the properties of states on $\mathscr P$ approach closer and closer to states on $R$ are identified and studied.

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English version:
Theoretical and Mathematical Physics, 1984, 59:1, 335–350

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Received: 09.09.1983

Citation: A. V. Voronin, V. N. Sushko, S. S. Horuzhy, “Algebras of unbounded operators and vacuum superselection rules in quantum field theory. I. Some properties of Op*-algebras and vector states on them”, TMF, 59:1 (1984), 28–48; Theoret. and Math. Phys., 59:1 (1984), 335–350

Citation in format AMSBIB
\Bibitem{VorSusHor84}
\by A.~V.~Voronin, V.~N.~Sushko, S.~S.~Horuzhy
\paper Algebras of unbounded operators and vacuum superselection rules in quantum field theory. I. Some properties of Op*-algebras and vector states on them
\jour TMF
\yr 1984
\vol 59
\issue 1
\pages 28--48
\mathnet{http://mi.mathnet.ru/tmf4703}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=749003}
\zmath{https://zbmath.org/?q=an:0559.47033}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 59
\issue 1
\pages 335--350
\crossref{https://doi.org/10.1007/BF01028511}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984TR03500002}


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    This publication is cited in the following articles:
    1. A. V. Voronin, V. N. Sushko, S. S. Horuzhy, “Algebras of unbounded operators and vacuum superselection rules in quantum field theory II. Mathematical structure of vacuum superselection rules”, Theoret. and Math. Phys., 60:3 (1984), 849–862  mathnet  crossref  mathscinet  zmath  isi
    2. A. V. Voronin, “Discrete vacuum superselection rule in Wightman theory with essentially self-adjoint field operators”, Theoret. and Math. Phys., 66:1 (1986), 8–19  mathnet  crossref  mathscinet  isi
    3. A. V. Voronin, S. S. Horuzhy, “$\mathrm{Op}^*$ and $\mathrm C^*$ dynamical systems I. Structural parallels”, Theoret. and Math. Phys., 82:2 (1990), 113–123  mathnet  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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