K. Yu. Dadashyan, S. S. Horuzhy, “Field algebras in quantum theory with indefinite metric. II. Formulation of a modular theory in Pontryagin space”, TMF, 62:1 (1985), 30–44; Theoret. and Math. Phys., 62:1 (1985), 21

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Teoreticheskaya i Matematicheskaya Fizika, 1985, Volume 62, Number 1, Pages 30–44 (Mi tmf4528)

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

Field algebras in quantum theory with indefinite metric. II. Formulation of a modular theory in Pontryagin space

K. Yu. Dadashyan, S. S. Horuzhy

Full-text PDF (1485 kB) Citations (7)

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Abstract: The formalism of modular theory for $J$-symmetric weakly closed algebras in Pontryagin space is introduced. Some propositions about the properties of the generalized $J$-Hilbert algebras $\mathscr U$ and $\mathscr U'$ are proved. The main tool in the proofs is the definitizing operator method.

Received: 13.03.1984

English version:
Theoretical and Mathematical Physics, 1985, Volume 62, Issue 1, Pages 21–30
DOI: https://doi.org/10.1007/BF01034821

Bibliographic databases:

Language: Russian

Citation: K. Yu. Dadashyan, S. S. Horuzhy, “Field algebras in quantum theory with indefinite metric. II. Formulation of a modular theory in Pontryagin space”, TMF, 62:1 (1985), 30–44; Theoret. and Math. Phys., 62:1 (1985), 21–30

Citation in format AMSBIB

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\paper Field algebras in quantum theory with indefinite metric. II.~Formulation of a~modular theory in Pontryagin space

\jour TMF

\yr 1985

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\pages 30--44

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\transl

\jour Theoret. and Math. Phys.

\yr 1985

\vol 62

\issue 1

\pages 21--30

\crossref{https://doi.org/10.1007/BF01034821}

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Linking options:

https://www.mathnet.ru/eng/tmf4528

https://www.mathnet.ru/eng/tmf/v62/i1/p30

Cycle of papers

On field algebras in quantum theory with indefinite metric
K. Yu. Dadashyan, S. S. Horuzhy
TMF, 1983, 54:1, 57–77
Field algebras in quantum theory with indefinite metric. II. Formulation of a modular theory in Pontryagin space
K. Yu. Dadashyan, S. S. Horuzhy
TMF, 1985, 62:1, 30–44
Field algebras in quantum theory with indefinite metric. III. Spectrum of modular operator and Tomita's fundamental theorem
K. Yu. Dadashyan, S. S. Horuzhy
TMF, 1987, 70:2, 181–191

This publication is cited in the following 7 articles:

E. V. Kissin, V. S. Shulman, “O predstavleniyakh grupp i algebr v prostranstvakh s indefinitnoi metrikoi”, Posvyaschaetsya pamyati professora N.D. Kopachevskogo, SMFN, 67, no. 2, Rossiiskii universitet druzhby narodov, M., 2021, 295–315
Victor S. Shulman, “Quasivectors and Tomita–Takesaki Theory for Operator Algebras on Π1-Spaces”, Rev. Math. Phys., 09:06 (1997), 749
S. N. Litvinov, “Bicyclic $WJ*$-algebras in Pontryagin space of type $\Pi_1$”, Funct. Anal. Appl., 26:3 (1992), 188–195
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
V. A. Shtraus, “On a bicyclic self-adjoint algebra in a Krein space that is non-isomorphic to its own commutator-group”, Russian Math. Surveys, 43:4 (1988), 239–240
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
K. Yu. Dadashyan, S. S. Horuzhy, “Field algebras in quantum theory with indefinite metric. IV”, Theoret. and Math. Phys., 72:3 (1987), 921–929

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	93
References:	45
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