Transformations of triangle ladder diagrams

Abstract

It is shown how dual space diagrammatic representation of momentum integrals corresponding to triangle ladder diagrams with an arbitrary number of rungs can be transformed to half-diamonds. In paper arXiv:0803.3420 [hep-th] the half-diamonds were related by conformal integral substitution to the diamonds which represent the dual space image of four-point ladder integrals in the four-dimensional momentum space. Acting in the way described in the present paper we do not need to use the known result for diamond (four-point) diagrams as an external input in deriving relations of arXiv:0803.3420 [hep-th], however, that result for the diamond diagram arises in the present proof as an intermediate consequence in a step-by-step diagrammatic transformation from the triangle ladder diagram to the half-diamond diagrams.

12 pages, 14 figures, Talk at "High energy physics in the LHC era" conference, Valparaiso,Chile, The XVIIth Oporto Meeting on Geometry, Topology and Physics "Mathematical aspects of quantum field theory", Oporto, Portugal; Revised version, Section 4 is enlarged, last paragraph in Conclusion is new, references added, second paragraph in Introduciton is modified

References in corpus (9)

• Magic identities for conformal four-point integrals
• Towards the two-loop Lcc vertex in Landau gauge
• New four-dimensional integrals by Mellin-Barnes transform
• Fourier transforms of UD integrals
• Triangle UD integrals in the position space
• Gluon self-interaction in the position space in Landau gauge
• Further results for the two-loop Lcc vertex in the Landau gauge
• On the Effective Action of Dressed Mean Fields for N = 4 Super-Yang-Mills Theory
• Semiclassical scattering amplitudes of dressed gravitons

Cited by in corpus (9)

• Exponential suppression with four legs and an infinity of loops
• Solution to Bethe-Salpeter equation via Mellin-Barnes transform
• New four-dimensional integrals by Mellin-Barnes transform
• Two-fold Mellin-Barnes transforms of Usyukina-Davydychev functions
• Belokurov-Usyukina loop reduction in non-integer dimension
• 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
• Alternative method of Reduction of the Feynman Diagrams to a set of Master Integrals