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Fourier transforms of UD integrals

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arxiv 0802.3468 v1 pith:GKUDRDZF submitted 2008-02-23 hep-th

Igor Kondrashuk , Anatoly Kotikov This is my paper · ORCID
classification hep-th
keywords functionsintegralsfourierintegralsecondspacetransformscalculated
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

UD integrals published by N. Usyukina and A. Davydychev in 1992-1993 are integrals corresponding to ladder-type Feynman diagrams. The results are UD functions $\Phi^{(L)},$ where $L$ is the number of loops. They play an important role in N=4 supersymmetic Yang-Mills theory. The integrals were defined and calculated in the momentum space. In this paper the position space representation of UD functions is investigated. We show that Fourier transforms of UD functions are UD functions of space-time intervals but this correspondence is indirect. For example, the Fourier transform of the second UD integral is the second UD integral.

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