Séminaire du 14 février 2011, 10h30: Flavia Stan,
Équipe-projet Algorithms, INRIA Paris-Rocquencourt.
A symbolic summation approach to Feynman integral calculus
We discuss two methods based on Wilf-Zeilberger summation for the
computation of Feynman parameter integrals.
For the first method, the integrals are rewritten as multisums of
hypergeometric terms to fit the input class of WZ-summation. These
summation problems are highly nested sums with non-standard boundary
conditions. They satisfy inhomogeneous recurrences containing sums of
lower nested depth on the right-hand sides. These last recurrences can be
solved recursively by Carsten Schneider’s Sigma package.
Another approach to evaluate Feynman integrals is by representing them as
nested Mellin-Barnes integrals. We show how WZ-methods determine
recurrences for contour integrals of this type, thus eliminating the need
to find sum representations. This algorithmic technique is also applied to
prove typical entries from the Gradshteyn-Ryzhik table of integrals using
the Mellin transform method.
This work is part of my PhD thesis, defended this year at RISC, Johannes
Kepler University Linz, Austria.
Virginie Collette
Last modified: Fri Feb 4 12:02:24 CET 2011