Properties of Feynman graph polynomials

Abstract

In this talk I discuss properties of the two Symanzik polynomials which characterise the integrand of an arbitrary multi-loop integral in its Feynman parametric form. Based on the construction from spanning forests and Laplacian matrices, Dodgson's relation is applied to derive factorisation identities involving both polynomials. An application of Whitney's 2-isomorphism theorem on matroids is discussed.

Comments: Talk given at the International Workshop 'Loops and Legs in Quantum Field Theory' (April 25-30, 2010, Wörlitz, Germany)