Methods of calculating many-loop diagrams and renormalization-group analysis of the~$\varphi^4$ theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 36 (1978) no. 2, pp. 271-278
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An effective technique is developed for calculating the renormalization-group parameters; this makes it possible to set all external momenta equal to zero in the calculation of diagrams. Three- and four-loop calculations of the Gell-Mann–Low function of the $\varphi^4$ theory are made in different renormalization schemes. The dependence of this function on the particular choice of fixed ratios of the momentum arguments of the invariant charge is investigated.
@article{TMF_1978_36_2_a10,
author = {A. A. Vladimirov},
title = {Methods of calculating many-loop diagrams and renormalization-group analysis of the~$\varphi^4$ theory},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {271--278},
publisher = {mathdoc},
volume = {36},
number = {2},
year = {1978},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1978_36_2_a10/}
}
TY - JOUR AU - A. A. Vladimirov TI - Methods of calculating many-loop diagrams and renormalization-group analysis of the~$\varphi^4$ theory JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1978 SP - 271 EP - 278 VL - 36 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1978_36_2_a10/ LA - ru ID - TMF_1978_36_2_a10 ER -
%0 Journal Article %A A. A. Vladimirov %T Methods of calculating many-loop diagrams and renormalization-group analysis of the~$\varphi^4$ theory %J Teoretičeskaâ i matematičeskaâ fizika %D 1978 %P 271-278 %V 36 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1978_36_2_a10/ %G ru %F TMF_1978_36_2_a10
A. A. Vladimirov. Methods of calculating many-loop diagrams and renormalization-group analysis of the~$\varphi^4$ theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 36 (1978) no. 2, pp. 271-278. http://geodesic.mathdoc.fr/item/TMF_1978_36_2_a10/