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 TMF, 1981, Volume 46, Number 1, Pages 27–32 (Mi tmf2294)

The singularities of Feynman diagrams in the coordinate space and the $\alpha$-representation

V. A. Smirnov

Abstract: The $\alpha$-representation is used to prove restrictions on the wave front of Feynman diagrams in the coordinate space, and also to establish the form of a singularity lying on the surface $\operatorname{det}S=0$ ($S$ is the matrix composed of the elements $s_{jj'}=(x_j-x_{j'})^2$) for the simplest diagram with four external vertices.

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English version:
Theoretical and Mathematical Physics, 1981, 46:1, 17–21

Bibliographic databases:

Citation: V. A. Smirnov, “The singularities of Feynman diagrams in the coordinate space and the $\alpha$-representation”, TMF, 46:1 (1981), 27–32; Theoret. and Math. Phys., 46:1 (1981), 17–21

Citation in format AMSBIB
\Bibitem{Smi81} \by V.~A.~Smirnov \paper The singularities of Feynman diagrams in the coordinate space and the $\alpha$-representation \jour TMF \yr 1981 \vol 46 \issue 1 \pages 27--32 \mathnet{http://mi.mathnet.ru/tmf2294} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=612469} \transl \jour Theoret. and Math. Phys. \yr 1981 \vol 46 \issue 1 \pages 17--21 \crossref{https://doi.org/10.1007/BF01019443} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MH85700002} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. A. Smirnov, “Singularities of feynman amplitudes in the momentum space”, Theoret. and Math. Phys., 47:1 (1981), 369–371
2. V. A. Smirnov, “Absolutely convergent $\alpha$ representation of analytically and dimensionally regularized Feynman amplitudes”, Theoret. and Math. Phys., 59:3 (1984), 563–573
3. A. I. Zaslavskii, “Behavior of massless feynman integrals near singular points”, Theoret. and Math. Phys., 80:3 (1989), 935–941
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