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arXiv · 2105.05948

Algebraic Interplay between Renormalization and Monodromy

Dirk Kreimer·Karen Yeats
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Abstract

We investigate combinatorial and algebraic aspects of the interplay between renormalization and monodromies for Feynman amplitudes. We clarify how extraction of subgraphs from a Feynman graph interacts with putting edges onshell or with contracting them to obtain reduced graphs. Graph by graph this leads to a study of cointeracting bialgebras. One bialgebra comes from extraction of subgraphs and hence is needed for renormalization. The other bialgebra is an incidence bialgebra for edges put either on- or offshell. It is hence related to the monodromies of the multivalued function to which a renormalized graph evaluates. Summing over infinite series of graphs, consequences for Green functions are derived using combinatorial Dyson--Schwinger equations.

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BibTeXRIS

Dirk Kreimer, Karen Yeats. 2021-05-12. Algebraic Interplay between Renormalization and Monodromy. https://doi.org/10.4310/atmp.2023.v27.n1.a4

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