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 TMF, 1971, Volume 9, Number 3, Pages 380–387 (Mi tmf4504)

On differential equations for the Feynman integral of a one-loop diagram Journal Theoretical and Mathematical Physics

V. A. Golubeva

Abstract: The Feynman integral $I(s,t)$ for one-loop diagram with four vertices is considered. With the aid of the Griffiths' method of differentiating rational differential forms with respect to the parameter, it is proved that $I(s,t)$ satisfies the system of two first order differential equations. From this system a hyperbolic partial differential equation for $I(s,t)$ is obtained, the main coefiicient of which vanishes on the Landau's manifold of the Feynman integral.

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English version:
Theoretical and Mathematical Physics, 1971, 9:3, 1210–1216

Bibliographic databases:

Citation: V. A. Golubeva, “On differential equations for the Feynman integral of a one-loop diagram Journal Theoretical and Mathematical Physics”, TMF, 9:3 (1971), 380–387; Theoret. and Math. Phys., 9:3 (1971), 1210–1216

Citation in format AMSBIB
\Bibitem{Gol71} \by V.~A.~Golubeva \paper On differential equations for the Feynman integral of a~one-loop diagram Journal Theoretical and Mathematical Physics \jour TMF \yr 1971 \vol 9 \issue 3 \pages 380--387 \mathnet{http://mi.mathnet.ru/tmf4504} \zmath{https://zbmath.org/?q=an:0226.35055} \transl \jour Theoret. and Math. Phys. \yr 1971 \vol 9 \issue 3 \pages 1210--1216 \crossref{https://doi.org/10.1007/BF01043411} 

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This publication is cited in the following articles:
1. V. A. Golubeva, “Some problems in the analytic theory of Feynman integrals”, Russian Math. Surveys, 31:2 (1976), 139–207
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