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.
Last modified: Fri Feb 4 12:02:24 CET 2011