
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
selfadjoint 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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Theoretical and Mathematical Physics, 1984, 59:1, 335–350
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Article 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 2848
\mathnet{http://mi.mathnet.ru/tmf4703}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=749003}
\zmath{https://zbmath.org/?q=an:0559.47033}
\transl
\jour Theoret. and Math. Phys.
\yr 1984
\vol 59
\issue 1
\pages 335350
\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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http://mi.mathnet.ru/eng/tmf4703 http://mi.mathnet.ru/eng/tmf/v59/i1/p28
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Cycle of 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 TMF, 1984, 59:1, 28–48
 Algebras of unbounded operators and vacuum superselection rules in quantum field theory II. Mathematical structure of vacuum superselection rules
A. V. Voronin, V. N. Sushko, S. S. Horuzhy TMF, 1984, 60:3, 323–343
This publication is cited in the following articles:

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

A. V. Voronin, “Discrete vacuum superselection rule in Wightman theory with essentially selfadjoint field operators”, Theoret. and Math. Phys., 66:1 (1986), 8–19

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

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