Search results for "Apéry's constant"

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Bhabha Scattering and a special pencil of K3 surfaces

2018

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 Ap\'ery--Fermi pencil, that was related to Ap\'ery'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.

Algebra and Number Theory14C22 14J28 34L25 14J81010308 nuclear & particles physicsPhysics::Medical PhysicsGeneral Physics and Astronomy01 natural sciencesApéry's constantLattice (module)Theoretical physicsMathematics - Algebraic GeometryMathematics::Algebraic Geometry0103 physical sciencesFOS: Mathematics010306 general physicsAlgebraic Geometry (math.AG)Mathematics::Symplectic GeometryMathematical PhysicsPencil (mathematics)Bhabha scatteringMathematics
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