{"title":"Bhabha scattering and a special pencil of K3 surfaces","authors":"Dino Festi, D. Straten","doi":"10.4310/CNTP.2019.V13.N2.A4","DOIUrl":null,"url":null,"abstract":"We study a pencil of K3 surfaces that appeared in the $2$-loop diagrams in Bhabha scattering. By analysing in detail the Picard lattice of the general and special members of the pencil, we identify the pencil with the celebrated Apery--Fermi pencil, that was related to Apery's proof of the irrationality of $\\zeta(3)$ through the work of F. Beukers, C. Peters and J. Stienstra. The same pencil appears miraculously in different and seemingly unrelated physical contexts.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":"1 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2018-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"20","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Number Theory and Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/CNTP.2019.V13.N2.A4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 20
Abstract
We study a pencil of K3 surfaces that appeared in the $2$-loop diagrams in Bhabha scattering. By analysing in detail the Picard lattice of the general and special members of the pencil, we identify the pencil with the celebrated Apery--Fermi pencil, that was related to Apery's proof of the irrationality of $\zeta(3)$ through the work of F. Beukers, C. Peters and J. Stienstra. The same pencil appears miraculously in different and seemingly unrelated physical contexts.
我们研究了在Bhabha散射的$2$-环图中出现的K3曲面铅笔。通过对铅笔一般成员和特殊成员的皮卡德格的详细分析，我们将铅笔与著名的阿佩里-费米铅笔相识别，这与阿佩里通过F. Beukers, C. Peters和J. Stienstra的工作证明$\zeta(3)$的无理性有关。同样一支铅笔奇迹般地出现在不同的、看似不相关的物理环境中。
期刊介绍：
Focused on the applications of number theory in the broadest sense to theoretical physics. Offers a forum for communication among researchers in number theory and theoretical physics by publishing primarily research, review, and expository articles regarding the relationship and dynamics between the two fields.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
