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 TMF, 1983, Volume 54, Number 1, Pages 78–88 (Mi tmf4365)

On random fields corresponding to the BBGKY, Vlasov, and Boltzmann hierarchies

V. P. Maslov, A. M. Chebotarev

Abstract: A‘correspondence is established between the creation and annihilation operators introduced by Maslov and Tariverdiev [10] for the densities of the Bogolyubov and Boltzmann hierarchies and the transformations of the measures of the random fields associated with the hierarchies. Bogolyubov’s equation in variational derivatives for the moment functional of the hierarchies [1] is replaced by an equation for the characteristic functional, which is an infinite-dimensional Fourier transform of a measure. The measures of the random fields of the hierarchies satisfy infinitedimensional analogs of the known equations. These equations are written down by means of creation and annihilation operators acting on functionals and measures.

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English version:
Theoretical and Mathematical Physics, 1983, 54:1, 48–55

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Citation: V. P. Maslov, A. M. Chebotarev, “On random fields corresponding to the BBGKY, Vlasov, and Boltzmann hierarchies”, TMF, 54:1 (1983), 78–88; Theoret. and Math. Phys., 54:1 (1983), 48–55

Citation in format AMSBIB
\Bibitem{MasChe83} \by V.~P.~Maslov, A.~M.~Chebotarev \paper On random fields corresponding to the~BBGKY, Vlasov, and Boltzmann hierarchies \jour TMF \yr 1983 \vol 54 \issue 1 \pages 78--88 \mathnet{http://mi.mathnet.ru/tmf4365} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=704010} \transl \jour Theoret. and Math. Phys. \yr 1983 \vol 54 \issue 1 \pages 48--55 \crossref{https://doi.org/10.1007/BF01017123} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1983RF77900006} 

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

This publication is cited in the following articles:
1. V. P. Maslov, “Asymptotics of the solutions to the $N$-particle Kolmogorov-Feller equations and the asymptotics of the solution to the Boltzmann equation in the region of large”, Math. Notes, 58:5 (1995), 1166–1177
2. Yu. G. Kondrat'ev, A. M. Chebotarev, “Bernstein theorems and transformations of correlation measures in statistical physics”, Math. Notes, 79:5 (2006), 649–663
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