A symbolic summation approach to Feynman integral calculus

par Flavia Stan (INRIA Rocquencourt, Centre INRIA-Microsoft Research)

jeudi 8 déc. 2011, 10:30 → 11:30 Europe/Paris

XR.203 (Bâtiment XLIM)

We discuss two methods based on Wilf-Zeilberger summation motivated by 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. 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.