Loop Amplitudes and Quantum Homotopy Algebras

TL;DR

This paper introduces a recursive method for calculating loop-level scattering amplitudes in quantum field theories, based on quantum homotopy algebra structures, providing new insights into amplitude relations.

Contribution

It generalizes the tree-level recursion to loop levels using quantum homotopy algebras, offering a novel algebraic approach to amplitude computations.

Findings

Derived a recursion relation for loop amplitudes

Connected non-planar and planar amplitude relations

Applied homological perturbation lemma to quantum field theory

Abstract

We derive a recursion relation for loop-level scattering amplitudes of Lagrangian field theories that generalises the tree-level Berends-Giele recursion relation in Yang-Mills theory. The origin of this recursion relation is the homological perturbation lemma, which allows us to compute scattering amplitudes from minimal models of quantum homotopy algebras in a recursive way. As an application of our techniques, we give an alternative proof of the relation between non-planar and planar colour-stripped scattering amplitudes.