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.
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