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Picard-Fuchs equations for Feynman integrals

Stefan Müller-Stach, Stefan Weinzierl, Raphael Zayadeh

Number 20
Authors Stefan Müller-Stach
Raphael Zayadeh
Year 2012

We present a systematic method to derive an ordinary differential equation for any Feynman integral, where the differentiation is with respect to an external variable. The resulting differential equation is of Fuchsian type. The method can be used within fixed integer space-time dimensions as well as within dimensional regularisation. We show that finding the differential equation is equivalent to solving a linear system of equations. We observe interesting factorisation properties of the D-dimensional Picard-Fuchs operator when D is specialised to integer dimensions.

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