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 TMF, 1981, Volume 46, Number 2, Pages 199–212 (Mi tmf2330)

In frared and ultraviolet divergences of the coefficient functions of Feynman diagrams as tempered distributions. II

V. A. Smirnov

Abstract: The results of the author are generalized to the case of nonsealar Feynman diagrams. It is shown that the analytically regularized coefficient function $F_\Gamma(\underline q)$ associated with an arbitrary graph $\Gamma$ is a functional in $S'(R^{4k})$ and an analytic function of the regularizing parameters $\lambda_l$ in some nonempty domain, from which it can be continued to the whole of $C^L$ as a meromorphic function with two series of poles (infrared and ultraviolet). Conditions under which the coefficient functions have no infrared divergences as functionals in $S'$ are obtained. It is shown how and under what conditions a coefficient function can be defined as a functional on a subspace of $S(R^{4k})$.

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English version:
Theoretical and Mathematical Physics, 1981, 46:2, 132–140

Bibliographic databases:

Citation: V. A. Smirnov, “In frared and ultraviolet divergences of the coefficient functions of Feynman diagrams as tempered distributions. II”, TMF, 46:2 (1981), 199–212; Theoret. and Math. Phys., 46:2 (1981), 132–140

Citation in format AMSBIB
\Bibitem{Smi81} \by V.~A.~Smirnov \paper In frared and ultraviolet divergences of the coefficient functions of Feynman diagrams as tempered distributions.~II \jour TMF \yr 1981 \vol 46 \issue 2 \pages 199--212 \mathnet{http://mi.mathnet.ru/tmf2330} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=612955} \transl \jour Theoret. and Math. Phys. \yr 1981 \vol 46 \issue 2 \pages 132--140 \crossref{https://doi.org/10.1007/BF01030847} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981NE30200005} 

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This publication is cited in the following articles:
1. S. A. Anikin, V. A. Smirnov, “Analytic renormalization of massless theories”, Theoret. and Math. Phys., 51:1 (1982), 317–321
2. V. A. Smirnov, K. G. Chetyrkin, “Dimensional regularization and infrared divergences”, Theoret. and Math. Phys., 56:2 (1983), 770–776
3. V. A. Smirnov, “Absolutely convergent $\alpha$ representation of analytically and dimensionally regularized Feynman amplitudes”, Theoret. and Math. Phys., 59:3 (1984), 563–573
4. S. A. Anikin, V. A. Smirnov, “The R operation in theories with massless particles”, Theoret. and Math. Phys., 60:1 (1984), 664–670
5. V. A. Smirnov, K. G. Chetyrkin, “$R^*$ operation in the minimal subtraction scheme”, Theoret. and Math. Phys., 63:2 (1985), 462–469
6. A. I. Zaslavskii, “Behavior of massless feynman integrals near singular points”, Theoret. and Math. Phys., 80:3 (1989), 935–941
7. É. Yu. Lerner, “Feynman integrals of $p$-adic argument in momentum space III. Renormalization”, Theoret. and Math. Phys., 106:2 (1996), 195–208
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