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Transformations of triangle ladder diagrams
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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.
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A simple way to reduce the number of contours in the multi-fold Mellin-Barnes integrals
A five-fold Mellin-Barnes integral for the massless box diagram is reduced to a two-fold triangle integral using analytical regularization and residue calculus, without Barnes lemmas.
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