2008/02/23 by Igor Kondrashuk, A. V. Kotikov, Anatoly Kotikov · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #hep-th
paper · pdf · doi:10.1007/978-3-7643-9906-1_15
published as Analysis and Mathematical Physics, Trends in Mathematics, Birkhauser Verlag Basel (2009) 337-347 · 12 pages, 12 figures,
arxiv created 2008/02/23 · openalex publication_date 2009/01/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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 Φ ( L ) where L is the number of loops. They play an important role in N =4 supersymmetric 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 second UD integral is the second UD integral.