Bhabha散射和K3表面的特殊铅笔

IF 1.2 3区数学 Q1 MATHEMATICS

Communications in Number Theory and Physics Pub Date : 2018-09-13 DOI:10.4310/CNTP.2019.V13.N2.A4

Dino Festi, D. Straten

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引用次数: 20

摘要

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。

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Bhabha scattering and a special pencil of K3 surfaces

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.

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来源期刊

Communications in Number Theory and Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

>12 weeks

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.