indico System maintenance at: Thursday, February 12th, 2026, 13:00 - 22:00

1–5 Sept 2025
Bethe Center for Theoretical Physics
Europe/Berlin timezone

Surprising Evasions of Elliptic Obstructions

5 Sept 2025, 09:30
1h
Seminar Room bctp (Bethe Center for Theoretical Physics)

Seminar Room bctp

Bethe Center for Theoretical Physics

Speaker

David Broadhurst

Description

In 1968, I met an elliptic integral when studying the decay of the eta meson. Then it was a surprise to find that elliptic integrals are not needed for the magnetic moment of the electron at two loops. In 1998, I expected elliptic obstructions when evaluating three-loop massive vacuum diagrams. Yet empirical fits to numerical integrations gave results in terms of polylogarithms. Recently I have found more examples, where integrals of elliptic integrals multiplied by polylogarithms are empirically reducible to classical tetralogarithms. I shall describe how Steven Charlton and I have proved these results. The basic idea is to arrive at a double integral of dilogarithms and then remove an obstructing square root of a quartic polynomial by a pair of Euler transformations.

Presentation materials