Geodesic
Renormalized power of a generalized random field and equations for the Green's functions in the Euclidean domain
Teoretičeskaâ i matematičeskaâ fizika, Tome 17 (1973) no. 3, pp. 373-390 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The solvability of the Schwinger equations for the Green's functions in the Euclidean domain is investigated for definite types of selfinteraction of a single scalar field. It is shown that such equations can be solved and integral representations for the solution are found. 
@article{TMF_1973_17_3_a6,
     author = {N. S. Gonchar},
     title = {Renormalized power of a generalized random field and equations for the {Green's} functions in the {Euclidean} domain},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {373--390},
     year = {1973},
     volume = {17},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_17_3_a6/}
}
TY  - JOUR
AU  - N. S. Gonchar
TI  - Renormalized power of a generalized random field and equations for the Green's functions in the Euclidean domain
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1973
SP  - 373
EP  - 390
VL  - 17
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1973_17_3_a6/
LA  - ru
ID  - TMF_1973_17_3_a6
ER  - 
%0 Journal Article
%A N. S. Gonchar
%T Renormalized power of a generalized random field and equations for the Green's functions in the Euclidean domain
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1973
%P 373-390
%V 17
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1973_17_3_a6/
%G ru
%F TMF_1973_17_3_a6
N. S. Gonchar. Renormalized power of a generalized random field and equations for the Green's functions in the Euclidean domain. Teoretičeskaâ i matematičeskaâ fizika, Tome 17 (1973) no. 3, pp. 373-390. http://geodesic.mathdoc.fr/item/TMF_1973_17_3_a6/

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

[2] K. Symanzik, “Euclidean Quantum Field Theory”, International school of Physics “Enrico Fermi”, Varena, 1968

[3] J. Ginibre, Seminar notes on Euclidean quantum field theory IHES (Bures sur Yvette), 1966; Lecture at Winter School (Karpacz), Warszawa, 1967

[4] I. M. Gelfand, N. Ya. Vilenkin, Obobschennye funktsii, vyp. 4, Fizmatgiz, 1961 | MR

[5] R. H. Cameron, Proc. Amer. Math. Soc., 2 (1951), 1 | DOI | MR

[6] N. S. Gonchar, Preprint ITF-72-45P, Kiev, 1972

[7] I. Segal, J. Funct. Anal., 4 (1969) | DOI | MR | Zbl

[8] E. S. Titchmarsh, Introduction to the theory of Fourier integrals, 2 nd Ed., Clarendon Press, Oxford, 1948 | MR

[9] I. I. Gikhman, A. V. Skorokhod, Vvedenie v teoriyu sluchainykh protsessov, «Nauka», 1965 | MR | Zbl

[10] E. Nelson, “A quartic interaction in two dimensions”, Proc. Conf. Math. Theory. Elem. Particles, MIT Press, 1966 | MR

[11] I. Segal, Ann. Math., 92 (1970), 462 | DOI | MR | Zbl

[12] N. S. Gonchar, Preprint ITP-72-64E, Kiev, 1972