From elliptic curves to Feynman integrals

Luise Adams, Ekta Chaubey, S. Weinzierl
{"title":"From elliptic curves to Feynman integrals","authors":"Luise Adams, Ekta Chaubey, S. Weinzierl","doi":"10.22323/1.303.0069","DOIUrl":null,"url":null,"abstract":"In this talk we discuss Feynman integrals which are related to elliptic curves. We show with the help of an explicit example that in the set of master integrals more than one elliptic curve may occur. The technique of maximal cuts is a useful tool to identify the elliptic curves. By a suitable transformation of the master integrals the system of differential equations for our example can be brought into a form linear in $\\varepsilon$, where the $\\varepsilon^0$-term is strictly lower-triangular. This system is easily solved in terms of iterated integrals.","PeriodicalId":140132,"journal":{"name":"Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2018)","volume":"49 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2018)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22323/1.303.0069","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3

Abstract

In this talk we discuss Feynman integrals which are related to elliptic curves. We show with the help of an explicit example that in the set of master integrals more than one elliptic curve may occur. The technique of maximal cuts is a useful tool to identify the elliptic curves. By a suitable transformation of the master integrals the system of differential equations for our example can be brought into a form linear in $\varepsilon$, where the $\varepsilon^0$-term is strictly lower-triangular. This system is easily solved in terms of iterated integrals.
从椭圆曲线到费曼积分
在这次演讲中,我们将讨论与椭圆曲线有关的费曼积分。我们用一个显式的例子说明,在主积分集合中可以出现多条椭圆曲线。极大切割技术是识别椭圆曲线的有效工具。通过对主积分进行适当的变换,本例的微分方程组可以转化为$\varepsilon$中的线性形式,其中$\varepsilon^0$项是严格的下三角项。这个方程组很容易用迭代积分来求解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信