Learning scattering amplitudes by heart

TL;DR

This paper explores a novel mathematical framework connecting scattering amplitudes to advanced concepts in algebraic geometry and category theory, providing a new perspective on the structure of planar Feynman diagrams.

Contribution

It introduces a new interpretation of scattering amplitudes using canonical forms, projective masses, and cluster categories, bridging physics and higher algebra.

Findings

Establishes a link between scattering amplitudes and derived categories of quiver representations.

Provides a categorical interpretation of canonical forms in scattering amplitudes.

Connects cluster tilting objects with physical quantities in quantum field theory.

Abstract

The canonical forms associated to scattering amplitudes of planar Feynman diagrams are interpreted in terms of masses of projectives, defined as the modulus of their central charges, in the hearts of certain $t$-structures of derived categories of quiver representations and, equivalently, in terms of cluster tilting objects of the corresponding cluster categories.