Fourier transforms of UD integrals

Details Fourier transforms of UD integrals Fourier transforms of UD integrals

2008-02-23

arxiv.org/abs/0802.3468v1

Analysis and Mathematical Physics, Trends in Mathematics, Birkhauser Verlag Basel (2009) 337-347

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, 12 figures,

Scientific paper

10.1007/978-3-7643-9906-1_15

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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