Renormalization group and functional selfsimilarity in different branches of physics
Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 2, pp. 218-223 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A general formulation of “different” renormalization groups is given for different branches of physics-quantum field theory, the theory of kinetic phenomena, turbulence theory, polymer physics, the theory of radiative transfer. The unified formulation uses the language of group transformations and functional equations. The transformations and equations are based on a simple property, functional self-similarity, which is a generalization of ordinary self-similarity. The difference between the physical basis of the renormalization-group transformations in systems with infinitely large number of degrees of freedom and the functional self-similarity of simple physical systems is discussed.
@article{TMF_1984_60_2_a4,
     author = {D. V. Shirkov},
     title = {Renormalization group and functional selfsimilarity in different branches of physics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {218--223},
     year = {1984},
     volume = {60},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1984_60_2_a4/}
}
TY  - JOUR
AU  - D. V. Shirkov
TI  - Renormalization group and functional selfsimilarity in different branches of physics
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1984
SP  - 218
EP  - 223
VL  - 60
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1984_60_2_a4/
LA  - ru
ID  - TMF_1984_60_2_a4
ER  - 
%0 Journal Article
%A D. V. Shirkov
%T Renormalization group and functional selfsimilarity in different branches of physics
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1984
%P 218-223
%V 60
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1984_60_2_a4/
%G ru
%F TMF_1984_60_2_a4
D. V. Shirkov. Renormalization group and functional selfsimilarity in different branches of physics. Teoretičeskaâ i matematičeskaâ fizika, Tome 60 (1984) no. 2, pp. 218-223. http://geodesic.mathdoc.fr/item/TMF_1984_60_2_a4/

[1] Stueckelberg E., Petermann A., Helv. Phys. Acta, 26 (1953), 499–520 | MR | Zbl

[2] Gell-Mann M., Low F., Phys. Rev., 95 (1954), 1300–1312 | DOI | MR | Zbl

[3] Bogolyubov N. N., Shirkov D. V., DAN SSSR, 103 (1955), 203–206 | MR | Zbl

[4] Shirkov D. V., DAN SSSR, 105 (1955), 972–976

[5] Bogolyubov N. N., Shirkov D. V., DAN SSSR, 103 (1955), 391–394 | MR | Zbl

[6] Wilson K., Phys. Rev., B4 (1971), 3174–3183 ; 3184–3205 | DOI | Zbl | Zbl

[7] Kadanoff L. P., Physics, 2 (1966), 263–272

[8] De Dominicis C., Martin P., Phys. Rev., A19 (1979), 419–443 | DOI

[9] Pelletier G., J. Plasma Phys., 24 (1980), 421–443 | DOI

[10] De Zhen P., Idei skeilinga v fizike polimerov, Mir, M., 1982, 368 pp.

[11] Bell T., Frisch U., Frisch H., Phys. Rev., A17 (1978), 1049–1057 | DOI

[12] Mnatsakanyan M. A., Soobsch. Byurakan. obser., 1978, no. 50, 59–78

[13] Mnatsakanyan M. A., DAN SSSR, 262 (1982), 856–859 | MR

[14] Shirkov D. V., DAN SSSR, 263 (1982), 63–66 | MR

[15] Shirkov D. V., Preprint OIYaI E2-83-790, OIYaI, Dubna, 1983

[16] Ovsyannikov L. V., DAN SSSR, 109 (1956), 1112–1115 | MR

[17] Bogolyubov N. N., Shirkov D. V., Vvedenie v teoriyu kvantovannykh polei, Izd. 3-e, Nauka, M., 1976, 479 pp. ; Изд. 4-е, Наука, М., 1984, 605 с. | MR