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 Apéry-Fermi pencil, that was related to Apéry's proof of the irrationality of ζ(3) through the work of F. Beukers, C. Peters and J. Stienstra. The same pencil appears miraculously in different and seemingly unrelated physical contexts.
Bhabha scattering and a special pencil of K3 surfaces / Festi, D.; van Straten, D.. - In: COMMUNICATIONS IN NUMBER THEORY AND PHYSICS. - ISSN 1931-4523. - 13:2(2019), pp. 463-485. [10.4310/cntp.2019.v13.n2.a4]
Bhabha scattering and a special pencil of K3 surfaces
Festi, D.;
2019
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 Apéry-Fermi pencil, that was related to Apéry's proof of the irrationality of ζ(3) through the work of F. Beukers, C. Peters and J. Stienstra. The same pencil appears miraculously in different and seemingly unrelated physical contexts.| File | Dimensione | Formato | |
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