Geodesic
The method of diagrams in perturbation theory
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 29 (1974) no. 3, pp. 117-168

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{RM_1974_29_3_a4,
     author = {E. B. Gledzer and A. S. Monin},
     title = {The method of diagrams in perturbation theory},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {117--168},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {1974},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_1974_29_3_a4/}
}
TY  - JOUR
AU  - E. B. Gledzer
AU  - A. S. Monin
TI  - The method of diagrams in perturbation theory
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 1974
SP  - 117
EP  - 168
VL  - 29
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RM_1974_29_3_a4/
LA  - en
ID  - RM_1974_29_3_a4
ER  - 
%0 Journal Article
%A E. B. Gledzer
%A A. S. Monin
%T The method of diagrams in perturbation theory
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 1974
%P 117-168
%V 29
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RM_1974_29_3_a4/
%G en
%F RM_1974_29_3_a4
E. B. Gledzer; A. S. Monin. The method of diagrams in perturbation theory. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 29 (1974) no. 3, pp. 117-168. http://geodesic.mathdoc.fr/item/RM_1974_29_3_a4/