Geodesic
Bogolyubov generating functional method in statistical mechanics and the analog of the transformation to collective variables
Teoretičeskaâ i matematičeskaâ fizika, Tome 66 (1986) no. 3, pp. 463-480 
N. N. Bogolyubov (Jr.); A. K. Prikarpatskii. Bogolyubov generating functional method in statistical mechanics and the analog of the transformation to collective variables. Teoretičeskaâ i matematičeskaâ fizika, Tome 66 (1986) no. 3, pp. 463-480. http://geodesic.mathdoc.fr/item/TMF_1986_66_3_a12/
@article{TMF_1986_66_3_a12,
     author = {N. N. Bogolyubov (Jr.) and A. K. Prikarpatskii},
     title = {Bogolyubov generating functional method in statistical mechanics and the analog of the transformation to collective variables},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {463--480},
     year = {1986},
     volume = {66},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1986_66_3_a12/}
}
TY  - JOUR
AU  - N. N. Bogolyubov (Jr.)
AU  - A. K. Prikarpatskii
TI  - Bogolyubov generating functional method in statistical mechanics and the analog of the transformation to collective variables
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1986
SP  - 463
EP  - 480
VL  - 66
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1986_66_3_a12/
LA  - ru
ID  - TMF_1986_66_3_a12
ER  - 
%0 Journal Article
%A N. N. Bogolyubov (Jr.)
%A A. K. Prikarpatskii
%T Bogolyubov generating functional method in statistical mechanics and the analog of the transformation to collective variables
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1986
%P 463-480
%V 66
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1986_66_3_a12/
%G ru
%F TMF_1986_66_3_a12

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

]3ogolyubov's functional equations for the distribution functions in statistical mechanics for equilibrium and nonequilibrium many-particle systems are studied. An analog of the transformation to "collective" variables on the basis of an exact solution of ]3ogolyubov's functional equation in the equilibrium case is proposed. ]3ogolyubov's method is used to obtain a functional equation of Kirkwood-Salsburg-Symanzik type. A path integral method is developed for constructing the generating functionals of the distribution functions.

[1] Bogolyubov N. N. (ml.), Sadovnikov B. I., Izbrannye voprosy statisticheskoi fiziki, Vysshaya shkola, M., 1974

[2] Feinman R., Statisticheskaya mekhanika, Mir, M., 1977

[3] Bogolyubov N. N., Bogolyubov N. N. (ml.), Vvedenie v kvantovuyu statisticheskuyu mekhaniku, Nauka, M., 1984 | MR

[4] Bogolyubov N. N., Problemy dinamicheskoi teorii v statisticheskoi fizike, Gostekhizdat, M., 1946 | MR

[5] Menikoff R., Sharp D. H., J. Math. Phys., 19:1 (1978), 135–149 | DOI | MR

[6] Bogolyubov N. N., “Kvazisrednie v zadachakh statisticheskoi mekhaniki”, Izbr. tr., t. 2, Naukova dumka, Kiev, 1971, 174–243 | MR

[7] Minlos R. A., “Obobschennye sluchainye protsessy i ikh prodolzhenie do mery”, Tr. Mosk. matem. ob-va, 8, 1959, 497–518 | MR

[8] Bogolyubov N. N., “Uravneniya gidrodinamiki v statisticheskoi mekhanike”, Sb. tr. In-ta matem. AN USSR, 10, 1948, 41–59 | MR

[9] Bogolyubov N. N., “K voprosu o gidrodinamike sverkhtekuchei zhidkosti”, Izbr. tr., t. 3, Naukova dumka, Kiev, 1971, 244–270 | MR

[10] Gurov K. P., ZhETF, 18:1 (1948), 110–118 ; 20:3 (1950), 279–285 | MR | MR

[11] Yukhnovskii I. R., Golovko M. F., Statisticheskaya teoriya klassicheskikh ravnovesnykh sistem, Naukova dumka, Kiev, 1980 | MR

[12] Rebenko A. L., Uravneniya v funktsionalnykh proizvodnykh dlya funktsii raspredeleniya klassicheskoi statisticheskoi fiziki, Preprint No 77-56R, ITF AN USSR, Kiev, 1977

[13] Petrina D. Ya., Gerasimenko V. I., Malyshev P. V., Matematicheskie osnovy klassicheskoi statisticheskoi mekhaniki, Naukova dumka, Kiev, 1985 | MR | Zbl

[14] Frelikh Kh., Problemy teoreticheskoi fiziki, Sb., posvyaschennyi N. N. Bogolyubovu v svyazi s shestidesyatiletiem, Nauka, M., 1969, 373–384 | MR

[15] Bom D., Obschaya teoriya kollektivnykh peremennykh, Mir, M., 1964

[16] Zubarev D. N., DAN SSSR, 95:4 (1954), 757–760 | MR | Zbl

[17] Glimm Dzh., Dzhaffe A., Matematicheskie metody kvantovoi fiziki, Mir, M., 1984 | MR | Zbl

[18] Gallavotti G., Marchioro C., J. Math. Anal. Appl., 44 (1973), 661–675 | DOI | MR | Zbl

[19] Nelson E., J. Math. Phys., 5:3 (1964), 332–338 | DOI | MR

[20] Fröhlich J., Spencer T., J. Stat. Phys., 24:4 (1981), 617–701 | DOI | MR

[21] Brydges D. C., Commun. Math. Phys., 58:3 (1978), 313–350 | DOI | MR

[22] Brydges D. C., Tederbush P., Commun. Math. Phys., 73:2 (1980), 197–246 | DOI | MR

[23] Brydges D. C., Fröhlich J., Spencer T., Commun. Math. Phys., 83:2 (1982), 123–150 | DOI | MR

[24] Chen H. H., J. Phys. A: Math. Gen., 17:2 (1984), 197–209 | DOI | MR

[25] Berg M., Lefstrom I., Interpolyatsionnye prostranstva, Mir, M., 1980 | MR

[26] Popov V. N., Kontinualnye integraly v kvantovoi teorii polya i statisticheskoi fizike, Atomizdat, M., 1976 | MR

[27] Fedyanin V. K., Mochinsky B. V., Rodriguez C., Preprint E17-12850, JINR, Dubna, 1979

[28] Fradkin E. S., Problemy teoreticheskoi fiziki, Sb., posvyaschennyi N. N. Bogolyubovu v svyazi s shestidesyatiletiem, Nauka, M., 1969, 386–413 | MR

[29] Zubarev D. N., UFN, 21:1 (1960), 71–116 | DOI