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# Advances in Theoretical and Mathematical Physics

## Volume 27 (2023)

### Number 1

### Algebraic interplay between renormalization and monodromy

Pages: 87 – 191

DOI: https://dx.doi.org/10.4310/ATMP.2023.v27.n1.a4

#### Authors

#### 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.

Published 13 July 2023