Karlsruhe 2011 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 6: Quantum Field Theory I

MP 6.1: Hauptvortrag

Dienstag, 29. März 2011, 14:00–14:50, 30.45: 201

Feynman Graph Polynomials — •Christian Bogner — Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen

The integrand of any multi-loop integral in its Feynman parametric form is characterized by the first and the second Symanzik polynomial. These graph polynomials play a crucial role in current techniques for the computation of Feynman integrals as well as in recent formal researches related to periods in geometry. In this talk I review combinatorial properties of these polynomials, including their construction from spanning forests and from determinants of Laplacian matrices, their behaviour under the deletion/contraction of edges and Dodgson-type factorization identities. I furthermore discuss a certain application of matroid theory to the subject of Feynman integrals.