Abstract:
This article contains a survey of the research during the last decade on the analytic theory of Feynman integrals. We give a combinatorial definition of a Feynman integral, the explicit form of the simplest Feynman integrals, also the equations of their Landau varieties and a concise characterization of them. The main part of the article contains an investigation of the analytic and asymptotic properties of the Feynman integral of a single-loop diagram in the zero-spin theory of the interactions of particles: we give its expansion in a generalized hypergeometric series, the system of partial differential equations satisfied by it, and the ramification properties of the integral on a Landau variety. The problems solved for this integral allow us to pose a number of interesting problems for an arbitrary convergent Feynman integral.
\Bibitem{Gol76}
\by V.~A.~Golubeva
\paper Some problems in the analytic theory of Feynman integrals
\jour Russian Math. Surveys
\yr 1976
\vol 31
\issue 2
\pages 139--207
\mathnet{http://mi.mathnet.ru/eng/rm3682}
\crossref{https://doi.org/10.1070/RM1976v031n02ABEH001487}
\zmath{https://zbmath.org/?q=an:0334.28008|0342.28005}
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https://www.mathnet.ru/eng/rm3682
https://doi.org/10.1070/RM1976v031n02ABEH001487
https://www.mathnet.ru/eng/rm/v31/i2/p135
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