Geodesic
Dimensional renormalization in $p$-adic models of field theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 3, pp. 462-475 
É. Yu. Lerner; M. D. Missarov. Dimensional renormalization in $p$-adic models of field theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 3, pp. 462-475. http://geodesic.mathdoc.fr/item/TMF_2000_123_3_a7/
@article{TMF_2000_123_3_a7,
     author = {\'E. Yu. Lerner and M. D. Missarov},
     title = {Dimensional renormalization in $p$-adic models of field theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {462--475},
     year = {2000},
     volume = {123},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_123_3_a7/}
}
TY  - JOUR
AU  - É. Yu. Lerner
AU  - M. D. Missarov
TI  - Dimensional renormalization in $p$-adic models of field theory
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2000
SP  - 462
EP  - 475
VL  - 123
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2000_123_3_a7/
LA  - ru
ID  - TMF_2000_123_3_a7
ER  - 
%0 Journal Article
%A É. Yu. Lerner
%A M. D. Missarov
%T Dimensional renormalization in $p$-adic models of field theory
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2000
%P 462-475
%V 123
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2000_123_3_a7/
%G ru
%F TMF_2000_123_3_a7

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

We define fractional-dimensional $p$-adic Feynman amplitudes and construct a dimensional renormalization with minimum subtractions. In the fermionic model case, another dimensional renormalization procedure is defined as the inversion of the normalizing transformation at the trivial stable point for the hierarchical renormalization group transformation.

[1] E. Yu. Lerner, M. D. Missarov, Commun. Math. Phys., 121 (1989), 35–48 | DOI | MR | Zbl

[2] M. D. Missarov, “Renormalization group and renormalization theory in $p$-adic and adelic scalar models”, Dynamical Systems and Statistical Mechanics (Moscow, 1991), Adv. Sov. Math., 3, ed. Ya. G. Sinai, AMS, Providence, RI, 1991, 143–164 | MR

[3] E. Yu. Lerner, TMF, 106:2 (1996), 233–249 | DOI | MR | Zbl

[4] M. D. Missarov, Lett. Math. Phys., 32 (1994), 347–356 | DOI | MR | Zbl

[5] V. S. Vladimirov, I. V. Volovich, E. I. Zelenov, $p$-Adicheskii analiz i matematicheskaya fizika, Nauka, M., 1994 | MR

[6] M. D. Missarov, TMF, 109:1 (1996), 3–16 | DOI | MR | Zbl

[7] G. t'Hooft, M. Veltman, Nucl. Phys. B, 50 (1972), 318–353 | DOI | MR

[8] P. Breitenlohner, M. Mayson, Commun. Math. Phys., 52 (1977), 11–38 | DOI | MR

[9] E. Yu. Lerner, TMF, 102:3 (1995), 367–377 | MR | Zbl

[10] E. Yu. Lerner, TMF, 104:3 (1995), 371–392 | MR | Zbl

[11] E. Yu. Lerner, M. D. Missarov, J. Stat. Phys., 76:3/4 (1994), 805–817 | DOI | MR | Zbl

[12] M. D. Missarov, TMF, 118:1 (1999), 40–50 | DOI | MR | Zbl

[13] V. I. Arnold, Dopolnitelnye glavy teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1978 | MR

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

[15] V. A. Smirnov, Perenormirovka i asimptoticheskie razlozheniya feinmanovskikh amplitud, Izd-vo MGU, M., 1990 | MR