Coproducts of Multi-Loop Feynman Integrals

多环费曼积分的联积

• 批准号: 1853158
• 金额: --
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2016
• 资助国家: 英国
• 起止时间: 2016 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1853158
• 关键词: Coproducts; Multi; Loop; Feynman; Integrals

It is known that for one loop Feynman integrals there is a correspondence between a certain graphical coproduct and the coproduct of polylogarithms. It has recently been conjectured that the coproduct of a general integral may be expressed in a simple form (the so called master formula) involving master integrals and their corresponding contours. We seek to apply this idea to multi-loop Feynman integrals evaluating to Hypergeometric type functions to derive examples of a graphical coproduct beyond one loop. We will also explore the possible coproduct structure on elliptic functions required for the study of more general multi-loop integrals. Eventually it is hoped to obtain a fully general graphical coproduct for multi-loop integrals.

已知对单圈费曼积分，某个图形余积与多项式的余积之间存在对应关系。最近有人指出，一般积分的余积可以用一种简单的形式（所谓的主公式）表示，它包括主积分及其相应的轮廓。我们试图将这一想法应用到多圈费曼积分评估超几何型函数，以获得一个图形余积超过一个循环的例子。我们还将探讨更一般的多圈积分的研究所需的椭圆函数上可能的余积结构。最终希望得到一个完全通用的多圈积分的图形余积。

项目成果

Coaction for Feynman integrals and diagrams

• DOI: 10.22323/1.303.0047
• 发表时间: 2018-07
• 期刊: Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2018)
• 作者: S. Abreu;R. Britto;C. Duhr;E. Gardi;J. Matthew

Generalized hypergeometric functions and intersection theory for Feynman integrals

费曼积分的广义超几何函数和交集理论

• DOI: 10.22323/1.375.0067
• 发表时间: 2019
• 作者: Britto R

From positive geometries to a coaction on hypergeometric functions

从正几何到超几何函数的相互作用

• DOI: 10.1007/jhep02(2020)122
• 发表时间: 2020
• 期刊: Journal of High Energy Physics
• 影响因子: 5.4
• 作者: Abreu S

Diagrammatic Coaction of Two-Loop Feynman Integrals

二环费曼积分的图解相互作用

• DOI: 10.22323/1.375.0065
• 发表时间: 2019
• 作者: Matthew J