München 2009 – scientific programme

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T: Fachverband Teilchenphysik

T 25: Quantenfeldtheorie

T 25.4: Talk

Friday, March 13, 2009, 14:45–15:00, M010

Feynman graph polynomials and iterative algorithms — •Christian Bogner — Johannes Gutenberg-Universität Mainz

I briefly report on recent work with Stefan Weinzierl, where we have proven a theorem, stating that the Laurent coefficients of scalar Feynman integrals are periods in the sense of Kontsevich and Zagier, if they are evaluated at kinematical invariants taking rational values in Euclidean momentum space. Our proof uses the (extended) sector decomposition algorithm by Binoth and Heinrich. Our result is related to the appearance of multiple zeta values in coefficients of Feynman integrals which has recently been investigated by Francis Brown, using another iterative algorithm.

Both of these algorithms apply to the Feynman parametric representation of the integral and perform iterative manipulations of the polynomials in the integrand, which originate from the Symanzik polynomials. Motivated by the success of these methods I give a brief review on some more and some less well-known combinatorial properties of Symanzik polynomials. I focus on their accessibility to generalized theorems of the matrix-tree type and their relation to the multivariate Tutte polynomial.