Topology and geometry of elliptic Feynman amplitudes

TL;DR

This paper analytically computes the 2-loop Bhabha scattering amplitude in QED, exploring its structure and connections to hyperbolic Coxeter groups and elliptic curve geometries.

Contribution

It introduces a novel analysis linking the amplitude's structure to hyperbolic Coxeter groups and elliptic geometries, advancing understanding of quantum field theory amplitudes.

Findings

Analytic form of the 2-loop Bhabha scattering amplitude obtained.

Revealed connections to hyperbolic Coxeter groups.

Linked amplitude structure to elliptic curve geometries.

Abstract

We report on the analytic computation of the 2-loop amplitude for Bhabha scattering in QED. We study the analytic structure of the amplitude, and reveal its underlying connections to hyperbolic Coxeter groups and arithmetic geometries of elliptic curves.