
This article is cited in 4 scientific papers (total in 4 papers)
The method of diagrams in perturbation theory
E. B. Gledzer^{}, A. S. Monin^{}
Abstract:
In this paper the mathematical methods of quantum field theory are applied to some problems that arise in the statistical description of mechanical systems with very many (in the idealized case, infinitely many) degrees of freedom.
This application is based on a graphical representation of the individual terms of the formal perturbation series in powers of the coupling constant in the form of Feynman diagrams.
A variety of properties of such diagrams makes it possible to sum partially the perturbation series with a view to obtaining closed integral equations that contain the required quantities as unknowns. The approach is treated in more detail in connection with the statistical hydrodynamics of a developed turbulent flow, which is similar to the theory of a quantum Bose field with strong interaction.
The functional formulation of statistical hydrodynamics makes it possible to obtain integral equations of turbulence theory, which can also be derived by means of diagram methods. At the end of the paper, some closed equations of statistical hydrodynamics are considered.
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Russian Mathematical Surveys, 1974, 29:3, 117–168
Bibliographic databases:
UDC:
519.9
MSC: 76F30, 81Q30, 81Q15, 76D06 Received: 08.10.1973
Citation:
E. B. Gledzer, A. S. Monin, “The method of diagrams in perturbation theory”, Uspekhi Mat. Nauk, 29:3(177) (1974), 111–159; Russian Math. Surveys, 29:3 (1974), 117–168
Citation in format AMSBIB
\Bibitem{GleMon74}
\by E.~B.~Gledzer, A.~S.~Monin
\paper The method of diagrams in perturbation theory
\jour Uspekhi Mat. Nauk
\yr 1974
\vol 29
\issue 3(177)
\pages 111159
\mathnet{http://mi.mathnet.ru/umn4376}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=400985}
\zmath{https://zbmath.org/?q=an:0362.761020371.76048}
\transl
\jour Russian Math. Surveys
\yr 1974
\vol 29
\issue 3
\pages 117168
\crossref{https://doi.org/10.1070/RM1974v029n03ABEH001286}
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This publication is cited in the following articles:

V. P. Maslov, A. M. Chebotarev, “Generalized measure in Feynman path integrals”, Theoret. and Math. Phys., 28:3 (1976), 793–805

G. I. Babkin, V. I. Klyatskin, “Analysis of the Dyson equation for stochastic integral equations”, Theoret. and Math. Phys., 41:3 (1979), 1080–1086

A. S. Monin, “Geophysical turbulence”, Russian Math. Surveys, 38:4 (1983), 127–149

É. V. Teodorovich, “Diagram equations of the theory of fully developed turbulence”, Theoret. and Math. Phys., 101:1 (1994), 1177–1183

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