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TMF, 1983, Volume 54, Number 1, Pages 57–77 (Mi tmf4364)  

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

On field algebras in quantum theory with indefinite metric

K. Yu. Dadashyan, S. S. Horuzhy


Abstract: The paper consists of two parts. The first discusses the problem of formulating the algebraic approach directly in a space with indefinite metric. One of the possible ways of constructing a net of local field algebras $\mathscr F(O)$ in the $J$ space (Krein space) is considered; it is based on the Bisognano–Wichmann formalism. The second part establishes a number of properties of “$WJ^*$ algebras” (weakly closed algebras with $J$ involution and unit in the $J$ space); the algebras $\mathscr F(O)$ belong to this class. The methods of the proof use generalizations of the fundamental concepts of Tomita–Takesaki theory for algebras with $J$ involution.

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English version:
Theoretical and Mathematical Physics, 1983, 54:1, 35–48

Bibliographic databases:

Received: 29.09.1982

Citation: K. Yu. Dadashyan, S. S. Horuzhy, “On field algebras in quantum theory with indefinite metric”, TMF, 54:1 (1983), 57–77; Theoret. and Math. Phys., 54:1 (1983), 35–48

Citation in format AMSBIB
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\by K.~Yu.~Dadashyan, S.~S.~Horuzhy
\paper On field algebras in quantum theory with indefinite metric
\jour TMF
\yr 1983
\vol 54
\issue 1
\pages 57--77
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=704009}
\zmath{https://zbmath.org/?q=an:0519.47031|0536.47035}
\transl
\jour Theoret. and Math. Phys.
\yr 1983
\vol 54
\issue 1
\pages 35--48
\crossref{https://doi.org/10.1007/BF01017122}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1983RF77900005}


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    Citing articles on Google Scholar: Russian citations, English citations
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    Cycle of papers

    This publication is cited in the following articles:
    1. K. Yu. Dadashyan, S. S. Horuzhy, “Field algebras in quantum theory with indefinite metric. II. Formulation of a modular theory in Pontryagin space”, Theoret. and Math. Phys., 62:1 (1985), 21–30  mathnet  crossref  mathscinet  zmath  isi
    2. K. Yu. Dadashyan, S. S. Horuzhy, “Field algebras in quantum theory with indefinite metric. III. Spectrum of modular operator and Tomita's fundamental theorem”, Theoret. and Math. Phys., 70:2 (1987), 125–133  mathnet  crossref  mathscinet  zmath  isi
    3. K. Yu. Dadashyan, S. S. Horuzhy, “Field algebras in quantum theory with indefinite metric. IV”, Theoret. and Math. Phys., 72:3 (1987), 921–929  mathnet  crossref  mathscinet  zmath
    4. T. Ya. Azizov, S. S. Horuzhy, “Ghost number and ghost conjugation operators in the formalism of BRST quantization”, Theoret. and Math. Phys., 80:1 (1989), 671–679  mathnet  crossref  mathscinet  isi
    5. S. N. Litvinov, “Bicyclic $WJ*$-algebras in Pontryagin space of type $\Pi_1$”, Funct. Anal. Appl., 26:3 (1992), 188–195  mathnet  crossref  mathscinet  zmath  isi
    6. S. S. Horuzhy, “Rigorous Formulation of a $2D$ Conformal Model in the Fock–Krein Space: Construction of the Global $\operatorname{Op}J^*$-Algebra of Fields and Currents”, Theoret. and Math. Phys., 141:1 (2004), 1381–1397  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. M. S. Matveichuk, A. M. Ionova, “Positive projections as generators of $J$-projections of type (B)”, Lobachevskii J. Math., 26 (2007), 91–105  mathnet  zmath
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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