Algebraic interplay between renormalization and monodromy

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Advances in Theoretical and Mathematical Physics Pub Date : 2021-05-12 DOI:10.4310/ATMP.2023.v27.n1.a4
D. Kreimer, K. Yeats
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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.
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重整化与单态之间的代数相互作用
我们研究了费曼振幅的重整化和单态之间相互作用的组合和代数方面。我们阐明了如何从费曼图中提取子图与将边放在壳上或收缩它们以获得约简图的相互作用。一个图接一个图,这导致了对互作用双代数的研究。一个双代数来自子图的提取,因此需要进行重整化。另一个双代数是置于壳上或壳外的边的关联双代数。因此,它与重归一化图求值的多值函数的单态有关。对无穷级数的图求和,使用组合Dyson- Schwinger方程推导出Green函数的结果。
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来源期刊
Advances in Theoretical and Mathematical Physics
Advances in Theoretical and Mathematical Physics 物理-物理:粒子与场物理
CiteScore
2.20
自引率
6.70%
发文量
0
审稿时长
>12 weeks
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.
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