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Teoreticheskaya i Matematicheskaya Fizika, 1994, Volume 98, Number 1, Pages 12–28 (Mi tmf1397)  
This article is cited in 5 scientific papers (total in 5 papers)

Field of sine-Gordon type in spacetime of arbitrary dimension: Existence of the nelson measure

A. I. Kirillov

Moscow Power Engineering Institute (Technical University)
Full-text PDF (1247 kB) Citations (5)
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Abstract: A model of a field with bounded current density is investigated. It is shown that there exists an infinite-fold integral that determines a generating functional of the Schwinger functions. It is shown that this functional is the Fourier transform of a probability measure on the field trajectories that is concentrated in a Hilbert subspace of the space of tempered distributions of first order of singularity. It is shown that the field satisfies the strong regularity axiom of Osterwalder and Schrader.
Received: 22.01.1993
English version:
Theoretical and Mathematical Physics, 1994, Volume 98, Issue 1, Pages 8–19
DOI: https://doi.org/10.1007/BF01015118
Bibliographic databases:
Language: Russian
Citation: A. I. Kirillov, “Field of sine-Gordon type in spacetime of arbitrary dimension: Existence of the nelson measure”, TMF, 98:1 (1994), 12–28; Theoret. and Math. Phys., 98:1 (1994), 8–19
Citation in format AMSBIB
\Bibitem{Kir94}
\by A.~I.~Kirillov
\paper Field of sine-Gordon type in spacetime of arbitrary dimension: Existence of the nelson measure
\jour TMF
\yr 1994
\vol 98
\issue 1
\pages 12--28
\mathnet{http://mi.mathnet.ru/tmf1397}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1291363}
\zmath{https://zbmath.org/?q=an:0817.35094}
\transl
\jour Theoret. and Math. Phys.
\yr 1994
\vol 98
\issue 1
\pages 8--19
\crossref{https://doi.org/10.1007/BF01015118}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994NV61800002}
Linking options:
  • https://www.mathnet.ru/eng/tmf1397
  • https://www.mathnet.ru/eng/tmf/v98/i1/p12
    • This publication is cited in the following 5 articles:
    1. V. I. Bogachev, N. V. Krylov, M. Röckner, “Elliptic and parabolic equations for measures”, Russian Math. Surveys, 64:6 (2009), 973–1078  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    2. A. I. Kirillov, “Stochastic quantization using a kerneled Langevin equation”, Theoret. and Math. Phys., 115:1 (1998), 410–417  mathnet  mathnet  crossref  crossref  isi
    3. A. I. Kirillov, “Generating functionals of $S$-matrix and Schwinger functions in WN-analysis. I”, Theoret. and Math. Phys., 111:1 (1997), 395–404  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. A. I. Kirillov, “Sine-Gordon type field in spacetime of arbitrary dimension. II: Stochastic quantization”, Theoret. and Math. Phys., 105:2 (1995), 1329–1345  mathnet  crossref  mathscinet  zmath  isi  elib
    5. A. I. Kirillov, “Infinite-dimensional analysis and quantum theory as semimartingale calculus”, Russian Math. Surveys, 49:3 (1994), 43–95  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Full-text PDF :120
    References:91
    First page:1
     
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