{"title":"Algebraic interplay between renormalization and monodromy","authors":"D. Kreimer, K. Yeats","doi":"10.4310/ATMP.2023.v27.n1.a4","DOIUrl":null,"url":null,"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.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.4310/ATMP.2023.v27.n1.a4","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 11
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.
期刊介绍:
Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.