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Spanning forest polynomials and the transcendental weight of Feynman graphs

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arxiv 0910.5429 v1 pith:VIRTLBOH submitted 2009-10-28 math-ph math.MP

Francis Brown , Karen Yeats This is my paper · ORCID
classification math-phmath.MP
keywords graphstranscendentalweightfeynmanforestpolynomialsspanningcertain
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abstract

We give combinatorial criteria for predicting the transcendental weight of Feynman integrals of certain graphs in $\phi^4$ theory. By studying spanning forest polynomials, we obtain operations on graphs which are weight-preserving, and a list of subgraphs which induce a drop in the transcendental weight.

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  1. Graph integrals, Feynman periods, and single-valued multiple zeta values

    math.QA 2026-07 conditional novelty 7.0 of 10

    Canonical integrals of graphs with E=2V−2 equal RW integrals and evaluate to single-valued multiple zeta values, which are shown to lie in the space of Feynman periods.

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