The full text of this article is unavailable through your IP address: 18.216.57.57
Contents Online
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