Geodesic
Feynman integrals of $p$-adic argument in momentum space III. Renormalization
Teoretičeskaâ i matematičeskaâ fizika, Tome 106 (1996) no. 2, pp. 233-249 
É. Yu. Lerner. Feynman integrals of $p$-adic argument in momentum space III. Renormalization. Teoretičeskaâ i matematičeskaâ fizika, Tome 106 (1996) no. 2, pp. 233-249. http://geodesic.mathdoc.fr/item/TMF_1996_106_2_a4/
@article{TMF_1996_106_2_a4,
     author = {\'E. Yu. Lerner},
     title = {Feynman integrals of $p$-adic argument in momentum {space~III.} {Renormalization}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {233--249},
     year = {1996},
     volume = {106},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_106_2_a4/}
}
TY  - JOUR
AU  - É. Yu. Lerner
TI  - Feynman integrals of $p$-adic argument in momentum space III. Renormalization
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1996
SP  - 233
EP  - 249
VL  - 106
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1996_106_2_a4/
LA  - ru
ID  - TMF_1996_106_2_a4
ER  - 
%0 Journal Article
%A É. Yu. Lerner
%T Feynman integrals of $p$-adic argument in momentum space III. Renormalization
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1996
%P 233-249
%V 106
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1996_106_2_a4/
%G ru
%F TMF_1996_106_2_a4

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

The ultraviolet and infrared sequences of the poles for the massless Feynman integrals of $p$-adic argument with the arbitrary power of propagators are found. Within the framework of MS-scheme for the analytic $R^*$-operation it is proved that the renormalized amplitudes are finite. Simple formulas for the calculation of counterterms (vertex parts) in coordinate and momentum spaces are given.

[1] Vladimirov V. S., Volovich I. V., Zelenov E. I., $P$-adicheskii analiz i matematicheskaya fizika, Nauka, M., 1994 | MR

[2] Brekke L., Freund P. G. O., Phys. Rep., 233:1 (1993), 1–66 | DOI | MR

[3] Bogolyubov N. N., Shirkov D. V., Vvedenie v teoriyu kvantovannykh polei, Nauka, M., 1984 | MR

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

[5] Missarov M. D., Dynamical systems and statistical mechanics, Adv. Sov. Math., 3, ed. Ya. G. Sinai, Amer. Matn. Soc., 1991, 143–161 | MR

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

[7] Smirnov V. A., Commun. Math. Phys., 149 (1992), 623–636 | DOI | MR | Zbl

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

[9] Smirnov V. A., Mod. Phys. Lett. A, 6 (1991), 1421–1427 | DOI | MR | Zbl

[10] Missarov M. D., Lett. in Math. Phys., 27 (1993), 149–154 | DOI | MR | Zbl

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

[12] Speer E. R., Ann. Inst. H. Poincare, 23 (1973), 1–21 | MR

[13] Blekher P. M., Preprint IPM AN SSSR No 117, M., 1979; Rep. Math. Phys., 19 (1984), 117 | DOI | MR

[14] Smirnov V. A., TMF, 44:3 (1980), 307–320 ; 46:2 (1981), 199–212 | MR | MR

[15] Anikin S. A., Zavyalov O. I., Karchev N. I., TMF, 44:3 (1980), 291–305 ; 46:1 (1981), 3–26 | MR | MR

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

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

[18] Tatt U. T., Teoriya grafov, Mir, M., 1988 | MR

[19] Smirnov V. A., Chetyrkin K. G., Preprint NIIYaF MGU 89-2/79, M., 1989