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Spanning Forest Polynomials and the Transcendental Weight of Feynman Graphs

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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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Authors and Affiliations

  1. Institut de Math. de Jussieu Paris, UMR 7586, Univ. Pierre et Marie Curie-Paris 6, F-75005, Paris, France

    Francis Brown

  2. Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 156, Canada

    Karen Yeats

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  1. Francis Brown
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  2. Karen Yeats
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Correspondence to Francis Brown.

Additional information

Communicated by A.Connes

Karen Yeats Supported by an NSERC discovery grant.

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Brown, F., Yeats, K. Spanning Forest Polynomials and the Transcendental Weight of Feynman Graphs. Commun. Math. Phys. 301, 357–382 (2011). https://doi.org/10.1007/s00220-010-1145-1

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  • DOI: https://doi.org/10.1007/s00220-010-1145-1

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