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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。
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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