Geodesic
The Hopf graph algebra and renormalization group equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 1, pp. 22-32 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the renormalization group equations implied by the Hopf graph algebra. The vertex functions are regarded as vectors in the dual space of the Hopf algebra. The renormalization group equations for these vertex functions are equivalent to those for individual Feynman integrals. The solution of the renormalization group equations can be represented in the form of an exponential of the beta function. We clearly show that the exponential of the one-loop beta function allows finding the coefficients of the leading logarithms for individual Feynman integrals. The calculation results agree with those obtained in the parquet approximation.
Keywords: Hopf graph algebra, renormalization group, leading logarithms. 
@article{TMF_2005_143_1_a2,
     author = {D. V. Malyshev},
     title = {The {Hopf} graph algebra and renormalization group equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {22--32},
     year = {2005},
     volume = {143},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_143_1_a2/}
}
TY  - JOUR
AU  - D. V. Malyshev
TI  - The Hopf graph algebra and renormalization group equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2005
SP  - 22
EP  - 32
VL  - 143
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2005_143_1_a2/
LA  - ru
ID  - TMF_2005_143_1_a2
ER  - 
%0 Journal Article
%A D. V. Malyshev
%T The Hopf graph algebra and renormalization group equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2005
%P 22-32
%V 143
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2005_143_1_a2/
%G ru
%F TMF_2005_143_1_a2
D. V. Malyshev. The Hopf graph algebra and renormalization group equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 143 (2005) no. 1, pp. 22-32. http://geodesic.mathdoc.fr/item/TMF_2005_143_1_a2/

[1] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, Nauka, M., 1976 ; Дж. Коллинз, Перенормировка, Мир, М., 1988 | MR | MR

[2] K. G. Chetyrkin, Nuovo Cimento A, 103 (1990), 1653 | DOI | MR

[3] A. Connes, D. Kreimer, Commun. Math. Phys., 210 (2000), 249 ; E-print hep-th/9912092 | DOI | MR | Zbl

[4] A. Connes, D. Kreimer, Commun. Math. Phys., 216 (2001), 215 ; E-print hep-th/0003188 | DOI | MR | Zbl

[5] D. Malyshev, Phys. Lett. B, 578 (2004), 231 ; E-print hep-th/0307301 | DOI | MR | Zbl

[6] D. Malyshev, Non RG logarithms via RG equations, E-print hep-th/0402074

[7] A. Connes, H. Moscovici, Commun. Math. Phys., 198 (1998), 199 ; ; A. Gerasimov, A. Morozov, K. Selivanov, Int. J. Mod. Phys. A, 16 (2001), 1531 ; E-print math.DG/9806109E-print hep-th/0005053 | DOI | MR | Zbl | DOI | MR | Zbl

[8] D. Kreimer, Adv. Theor. Math. Phys., 3:3 (1999), 627 ; E-print hep-th/9901099 | DOI | MR | Zbl

[9] A. M. Polyakov, ZhETF, 57 (1969), 271

[10] I. V. Volovich, D. V. Prokhorenko, Tr. MIRAN, 147, 2004, 166

[11] D. Malyshev, JHEP, 0205 (2002), 013 ; E-print hep-th/0112146 | DOI | MR

[12] V. A. Smirnov, E. R. Rakhmetov, TMF, 120:1 (1999), 64 ; ; V. A. Smirnov, Phys. Lett. B, 465 (1999), 226 ; E-print hep-ph/9812529E-print hep-ph/9907471 | DOI | Zbl | DOI