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 TMF, 1984, Volume 59, Number 3, Pages 373–387 (Mi tmf5023)

Absolutely convergent $\alpha$ representation of analytically and dimensionally regularized Feynman amplitudes

V. A. Smirnov

Abstract: An absolutely convergent $\alpha$ representation of analytically and (or) dimensionally regularized Feynman.amplitudes is obtained on different sections of the domain of analyticity with respect to the regularizing parameters. The representation differs from the $\alpha$ representation in the original domain of absolute convergence by the presence in the integrand of an operator $\mathscr R^*$, which has the same structure as the $R^*$ operation that generalizes dimensional renormalization when not only ultraviolet but also infrared poles are present. The operator $\mathscr R^*$ explicitly realizes analytic continuation of the parametric integral and can be expressed in terms of the ultraviolet subtracting operators and also in terms of the infrared subtracting operators that generate a Maclaurin expansion in the coordinate space.

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English version:
Theoretical and Mathematical Physics, 1984, 59:3, 563–573

Bibliographic databases:

Citation: V. A. Smirnov, “Absolutely convergent $\alpha$ representation of analytically and dimensionally regularized Feynman amplitudes”, TMF, 59:3 (1984), 373–387; Theoret. and Math. Phys., 59:3 (1984), 563–573

Citation in format AMSBIB
\Bibitem{Smi84} \by V.~A.~Smirnov \paper Absolutely convergent $\alpha$ representation of analytically and dimensionally regularized Feynman amplitudes \jour TMF \yr 1984 \vol 59 \issue 3 \pages 373--387 \mathnet{http://mi.mathnet.ru/tmf5023} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=759528} \transl \jour Theoret. and Math. Phys. \yr 1984 \vol 59 \issue 3 \pages 563--573 \crossref{https://doi.org/10.1007/BF01018195} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1984TY74200005} 

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This publication is cited in the following articles:
1. S. A. Anikin, V. A. Smirnov, “The R operation in theories with massless particles”, Theoret. and Math. Phys., 60:1 (1984), 664–670
2. V. A. Smirnov, K. G. Chetyrkin, “$R^*$ operation in the minimal subtraction scheme”, Theoret. and Math. Phys., 63:2 (1985), 462–469
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