Fourier transforms of UD integrals

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.

12 pages, 12 figures,

References in corpus (17)

• Gluon scattering amplitudes at strong coupling
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Magic identities for conformal four-point integrals
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• New Dual Conformally Invariant Off-Shell Integrals
• Towards the two-loop Lcc vertex in Landau gauge
• Effective action of dressed mean fields for N = 4 super-Yang-Mills theory
• QCD effective action with dressing functions - consistency checks in the perturbative regime
• An approach to solve Slavnov-Taylor identities in nonsupersymmetric non-Abelian gauge theories
• Renormalizations in softly broken N=1 theories: Slavnov-Taylor identities
• The solution to Slavnov-Taylor identities in D4 N=1 SYM
• An approach to solve Slavnov-Taylor identity in D4 N=1 supergravity
• Gluon self-interaction in the position space in Landau gauge
• On the Effective Action of Dressed Mean Fields for N = 4 Super-Yang-Mills Theory
• Further results for the two-loop Lcc vertex in the Landau gauge
• Finiteness of N =4 super-Yang-Mills effective action in terms of dressed N =1 superfields
• Semiclassical scattering amplitudes of dressed gravitons

Cited by in corpus (9)

• Solution to Bethe-Salpeter equation via Mellin-Barnes transform
• New four-dimensional integrals by Mellin-Barnes transform
• Transformations of triangle ladder diagrams
• Two-fold Mellin-Barnes transforms of Usyukina-Davydychev functions
• Box ladders in non-integer dimension
• Explicit calculation of multi-fold contour integrals of certain ratios of Euler gamma functions. Part 1
• Multi-fold contour integrals of certain ratios of Euler gamma functions from Feynman diagrams: orthogonality of triangles
• Convergence Arguments to Bridge Cauchy and Matérn Covariance Functions
• Alternative method of Reduction of the Feynman Diagrams to a set of Master Integrals