Double Box Motive

TL;DR

This paper demonstrates that the motive linked to the second Symanzik polynomial of the double-box two-loop Feynman graph with generic parameters is an elliptic curve, revealing a deep geometric structure in quantum field theory calculations.

Contribution

It establishes that the motive of the second Symanzik polynomial in this specific Feynman graph is an elliptic curve, connecting physics and algebraic geometry.

Findings

The motive is an elliptic curve.

Provides geometric insight into Feynman integrals.

Links quantum field theory to elliptic curve theory.

Abstract

The motive associated to the second Symanzik polynomial of the double-box two-loop Feynman graph with generic masses and momenta is shown to be an elliptic curve.