Feynman graph polynomials

2010/02/18 by Christian Bogner, Stefan Weinzierl · 1 voice
Mathematics · Physics and Astronomy · #hep-ph #math-ph #math.MP

paper · pdf · doi:10.1142/s0217751x10049438

35 pages, references added

arxiv published 2010/02/18 · arxiv created 2010/04/23 · arxiv updated 2010/04/23

Abstract

The integrand of any multi-loop integral is characterised after Feynman parametrisation by two polynomials. In this review we summarise the properties of these polynomials. Topics covered in this article include among others: Spanning trees and spanning forests, the all-minors matrix-tree theorem, recursion relations due to contraction and deletion of edges, Dodgson's identity and matroids.

Discussions

• There is a relation,, between the voltages at the nodes of a circuit and the number of spanning trees of the associated graph. If we write the node voltages as a column vector $(v_1,\ldots, v_n)^T$ an [stackexchange, 0 points]

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