Geodesic
Kirkwood–Salzburg equations for the coefficient functions of the $S$ matrix
Teoretičeskaâ i matematičeskaâ fizika, Tome 8 (1971) no. 3, pp. 369-380 
D. Ya. Petrina; V. I. Skripnik. Kirkwood–Salzburg equations for the coefficient functions of the $S$ matrix. Teoretičeskaâ i matematičeskaâ fizika, Tome 8 (1971) no. 3, pp. 369-380. http://geodesic.mathdoc.fr/item/TMF_1971_8_3_a8/
@article{TMF_1971_8_3_a8,
     author = {D. Ya. Petrina and V. I. Skripnik},
     title = {Kirkwood{\textendash}Salzburg equations for the coefficient functions of the $S$ matrix},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {369--380},
     year = {1971},
     volume = {8},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1971_8_3_a8/}
}
TY  - JOUR
AU  - D. Ya. Petrina
AU  - V. I. Skripnik
TI  - Kirkwood–Salzburg equations for the coefficient functions of the $S$ matrix
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1971
SP  - 369
EP  - 380
VL  - 8
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1971_8_3_a8/
LA  - ru
ID  - TMF_1971_8_3_a8
ER  - 
%0 Journal Article
%A D. Ya. Petrina
%A V. I. Skripnik
%T Kirkwood–Salzburg equations for the coefficient functions of the $S$ matrix
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1971
%P 369-380
%V 8
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1971_8_3_a8/
%G ru
%F TMF_1971_8_3_a8

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

A system of Kirkwood–Salzburg type equations is obtained for the coefficient functions of the $S$ matrix in the Euclidean region. The existence of solutions of the equations for the coefficient functions in the case of an infinite volume is proved for models of a real scalar field with bounded nonlinear Lagrangians. A study is made of the analogy between Euclidean quanturn field theory and statistical mechanics.

[1] K. Symanzik, J. Math. Phys., 7 (1966), 510 | DOI | MR

[2] J. Ginibre, J. Math. Phys., 6 (1965), 238 | DOI | MR | Zbl

[3] J. Schwinger, Phys. Rev., 115 (1959), 721 | DOI | MR | Zbl

[4] P. C. Martin, J. Schwinger, Phys. Rev., 115 (1959), 1342 ; P. Martin, Yu. Shvinger, Teoriya sistem mnogikh chastits, IL, 1962 | DOI | MR | Zbl

[5] N. N. Bogolyubov, B. I. Khatset, DAN SSSR, 66 (1949), 321 | MR | Zbl

[6] B. I. Khatset, Naukovi zapiski Zhitomirskogo pedagogichnogo institutu, fizmat seriya, 3, 113; (1956), 139

[7] N. N. Bogolyubov, D. Ya. Petrina, B. I. Khatset, TMF, 1 (1969), 251

[8] D. Ruelle, Ann. Phys., 25 (1963), 209 | DOI | MR

[9] D. Ruelle, Rev. Mod. Phys., 36 (1964), 580 | DOI | MR

[10] L. Van Hove, Physica, 15 (1949), 951 | DOI | Zbl

[11] C. N. Yang, T. D. Lee, Phys. Rev., 87 (1952), 404 | DOI | Zbl

[12] D. Ruelle, Helv. Phys. Acta, 36 (1963), 789 | MR | Zbl

[13] E. S. Fradkin, Nucl. Phys., 49 (1963), 624 | DOI | MR

[14] G. V. Efimov, TMF, 2 (1970), 302 | MR

[15] T. Khill, Statisticheskaya mekhanika, IL, 1960

[16] N. N. Bogolyubov, Problemy dinamicheskoi teorii v statisticheskoi fizike, GITTL, 1946 | MR