Geodesic
Analog of dimensional regularization for calculation of the renormalization-group functions in the $1/n$ expansion for arbitrary dimension of space
Teoretičeskaâ i matematičeskaâ fizika, Tome 55 (1983) no. 2, pp. 163-175 
A. N. Vasil'ev; M. Yu. Nalimov. Analog of dimensional regularization for calculation of the renormalization-group functions in the $1/n$ expansion for arbitrary dimension of space. Teoretičeskaâ i matematičeskaâ fizika, Tome 55 (1983) no. 2, pp. 163-175. http://geodesic.mathdoc.fr/item/TMF_1983_55_2_a0/
@article{TMF_1983_55_2_a0,
     author = {A. N. Vasil'ev and M. Yu. Nalimov},
     title = {Analog of dimensional regularization for calculation of the renormalization-group functions in the~$1/n$ expansion for arbitrary dimension of space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {163--175},
     year = {1983},
     volume = {55},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1983_55_2_a0/}
}
TY  - JOUR
AU  - A. N. Vasil'ev
AU  - M. Yu. Nalimov
TI  - Analog of dimensional regularization for calculation of the renormalization-group functions in the $1/n$ expansion for arbitrary dimension of space
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1983
SP  - 163
EP  - 175
VL  - 55
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1983_55_2_a0/
LA  - ru
ID  - TMF_1983_55_2_a0
ER  - 
%0 Journal Article
%A A. N. Vasil'ev
%A M. Yu. Nalimov
%T Analog of dimensional regularization for calculation of the renormalization-group functions in the $1/n$ expansion for arbitrary dimension of space
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1983
%P 163-175
%V 55
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1983_55_2_a0/
%G ru
%F TMF_1983_55_2_a0

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

The renormalization of the massless (critical) $O_n$-symmetric nonlinear $\sigma$, model for arbitrary dimension $2 of space is investigated. The introduction of analytic regularization makes it possible to calculate the renormalization constants and the anomalous dimensions directly in the framework of massless theory in the same way as in the $4-\varepsilon$ scheme of dimensional regularization of the $\varphi^4$.

[1] 'tHooft G., Veltman M., Nucl. Phys., B44:1 (1972), 189-2-13 ; 'tHooft G., Veltman M., Nucl. Phys., B61:2 (1973), 455–467 | DOI | MR | DOI

[2] Chetyrkin K. G., Kataev A. L., Tkachov F. F., Phys. Lett., 99B:2 (1981), 147–150 | DOI | MR

[3] Tarasov O. B., Vladimirov A. A., Preprint E2-80-483, JINR, Dubna, 1980

[4] Brezin E., Le Guillou J. G., Zinn-Justin J., Phase Transitions and Critical Phenomena, eds. C. Domb, M. Green, Akcademic Press, N.-Y., 1976 | MR

[5] Hikami S., Progr. Theor. Phys., 62:1 (1979), 226–233 | DOI

[6] Arefeva I. Ya., TMF, 29:2 (1976), 147–153 ; 31:1 (1977), 3–11 | MR | MR

[7] Bogolyubov N. N., Shirkov D. V., Vvedenie v teoriyu kvantovannykh polei, Nauka, M., 1976 | MR

[8] Vladimirov A. A., TMF, 36:2 (1978), 271–278 | MR

[9] Speer E. R., Generalized Feynman amplitudes, Princeton Univ. press; Univ. Tokyo press, Princeton, N.-Y., Tokyo, 1969 ; Annals of math. studies, no. 62 | MR

[10] Zavyalov O. I., Perenormirovannye diagrammy Feinmana, Nauka, M., 1979 | MR

[11] Vasilev A. V., Pismak Yu. M., Khonkonen Yu. R., TMF, 50:2 (1982), 195–206

[12] Okabe Y., Oku M., Abe R., Progr. Theor. Phys., 60:5 (1978), 1277–1297 ; Васильев А. В., Письмак Ю. М., Хонконен Ю. Р., ТМФ, 47:3 (1981), 291–306 | DOI