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Mat. Zametki, 1978, Volume 23, Issue 1, Pages 113–119 (Mi mz8124)  

This article is cited in 2 scientific papers (total in 2 papers)

The differential equations for the feynman amplitude of a single-loop graph with four vertices

V. A. Golubeva, V. Z. Ènol'skii

Institute of Theoretical Physics, Academy of Sciences of the Ukrainian SSR, USSR

Abstract: A system of second-order partial differential equations for the Feynman amplitude of a single-loop graph with four vertices is obtained. It is proved that the symbol of differential operators of this system is singular (in the sense of I. N. Bernshtein) on the Landau manifold of the Feynman amplitude under consideration. The derived system of differential equations is a multidimensional generalization of the system of differential equations for the hypergeometric function of two variables of Appell and Kampé de Fériet.

Full text: PDF file (481 kB)

English version:
Mathematical Notes, 1978, 23:1, 63–66

Bibliographic databases:

UDC: 517,9
Received: 20.01.1975

Citation: V. A. Golubeva, V. Z. Ènol'skii, “The differential equations for the feynman amplitude of a single-loop graph with four vertices”, Mat. Zametki, 23:1 (1978), 113–119; Math. Notes, 23:1 (1978), 63–66

Citation in format AMSBIB
\Bibitem{GolEno78}
\by V.~A.~Golubeva, V.~Z.~\`Enol'skii
\paper The differential equations for the feynman amplitude of a single-loop graph with four vertices
\jour Mat. Zametki
\yr 1978
\vol 23
\issue 1
\pages 113--119
\mathnet{http://mi.mathnet.ru/mz8124}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=487267}
\zmath{https://zbmath.org/?q=an:0404.35062|0369.35054}
\transl
\jour Math. Notes
\yr 1978
\vol 23
\issue 1
\pages 63--66
\crossref{https://doi.org/10.1007/BF01104888}


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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. Golubeva, “On systems with regular singularities, and their solutions”, Math. USSR-Izv., 27:1 (1986), 27–38  mathnet  crossref  mathscinet  zmath
    2. V. A. Golubeva, “On the Regge–Gelfand problem of construction of a Pfaff system of Fuchsian type with a given singular divisor”, Journal of Mathematical Sciences, 202:5 (2014), 653–666  mathnet  crossref
  • Математические заметки Mathematical Notes
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