Feynman integral for exponential interaction in four-dimensional space-time. I
Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 3, pp. 307-314 Cet article a éte moissonné depuis la source Math-Net.Ru

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By means of the change of variables $\varphi(x)\to{:}\exp\varphi(x){:}_{1+3}+\text{ counterterms}$ a countably additive measure is constructed on the space of Gel'fand–Shilov–Jaffe generalized functions, and it is used to obtain an integral representation for the Green's functions of quantum field theory with the interaction ${:}\exp\varphi{:}_{1+3}$ without ultraviolet cutoff (and with a space-time cutoff).
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È. P. Osipov. Feynman integral for exponential interaction in four-dimensional space-time. I. Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 3, pp. 307-314. http://geodesic.mathdoc.fr/item/TMF_1981_47_3_a1/

[1] Saimon B., Model $P(\varphi)_2$ evklidovoi kvantovoi teorii polya, Mir, M., 1976

[2] Gachok V. P., Kvantovye protsessy, Naukova dumka, Kiev, 1975 | MR

[3] Malyshev V. A., “Veroyatnostnye aspekty kvantovoi teorii polya”, Itogi nauki i tekhniki. Teoriya veroyatnostei. Matematicheskaya statistika. Teoreticheskaya kibernetika, 14, VINITI, M., 1977, 41–79 | MR | Zbl

[4] Konstruktivnaya teoriya polya, Sb. statei, Mir, M., 1977 | MR

[5] Evklidova kvantovaya teoriya polya. Markovskii podkhod, Sb. statei, Mir, M., 1978 | MR

[6] Petrina D. Ya., Ivanov S. S., Rebenko A. L., Uravneniya dlya koeffitsientnykh funktsii matritsy rasseyaniya, Nauka, M., 1979 | MR

[7] Osipov E. P., Preprint TF-102, Institut matematiki SO AN SSSR, Novosibirsk, 1979

[8] Gelfand I. M., Shilov G. E., Prostranstva osnovnykh i obobschennykh funktsii, Obobschennye funktsii, vyp. 2, Fizmatgiz, M., 1958 | MR

[9] Robertson A. P., Robertson V. Dzh., Topologicheskie vektornye prostranstva, Mir, M., 1967 | MR | Zbl

[10] Pich A., Yadernye lokalno vypuklye prostranstva, Mir, M., 1967 | MR

[11] Constantinescu F., Thalheimer W., “Euclidean Green's functions for Jaffe fields”, Commun. Math. Phys., 38:4 (1974), 299–316 | DOI | MR | Zbl

[12] Zhevlakov K. A., Slinko A. M, Shestakov I. P., Shirshov A. I., Koltsa, blizkie k assotsiativnym, Nauka, M., 1978 | MR | Zbl

[13] Borchers H. J., Yngvason J., “Necessary and sufficient conditions for integral representations of Wightman functionals at Schwinger points”, Commun. Math. Phys., 47:3 (1976), 197–213 | DOI | MR | Zbl

[14] Shefer Kh., Topologicheskie vektornye prostranstva, Mir, M., 1971 | MR

[15] Gelfand I. M., Vilenkin N. Ya., Nekotorye primeneniya garmonicheskogo analiza. Osnaschennye gilbertovy prostranstva, Obobschennye funktsii. vyp. 4, Fizmatgiz, M., 1961 | MR

[16] Bogolyubov N. N., Shirkov D. V., Vvedenie v teoriyu kvantovannykh polei, Nauka, M., 1973 | MR | Zbl

[17] Slavnov A. A., Faddeev L. D., Vvedenie v kvantovuyu teoriyu kalibrovochnykh polei, Nauka, M., 1978 | MR

[18] Efimov G. V., Nelokalnye vzaimodeistviya kvantovannykh polei, Nauka, M., 1977 | MR

[19] Volkov M. K., Pervushin V. N., Suschestvenno nelineinye kvantovye teorii, dinamicheskie simmetrii i fizika mezonov, Atomizdat, M., 1978