Feynman integral for exponential interaction in four-dimensional space-time.~I
Teoretičeskaâ i matematičeskaâ fizika, Tome 47 (1981) no. 3, pp. 307-314
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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).
@article{TMF_1981_47_3_a1,
author = {\`E. P. Osipov},
title = {Feynman integral for exponential interaction in four-dimensional {space-time.~I}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {307--314},
publisher = {mathdoc},
volume = {47},
number = {3},
year = {1981},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1981_47_3_a1/}
}
TY - JOUR AU - È. P. Osipov TI - Feynman integral for exponential interaction in four-dimensional space-time.~I JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1981 SP - 307 EP - 314 VL - 47 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1981_47_3_a1/ LA - ru ID - TMF_1981_47_3_a1 ER -
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/