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arxiv: 0802.3468 · v1 · submitted 2008-02-23 · ✦ hep-th

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Fourier transforms of UD integrals

Igor Kondrashuk , Anatoly Kotikov
Authors on Pith no claims yet
classification ✦ hep-th
keywords functionsintegralsfourierintegralsecondspacetransformscalculated
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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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    Modified inverse Laplace and Mellin transforms are proposed to work with dual contour integral representations from quantum chromodynamics for quantum communication applications.