Geometry and causal flux in multi-loop Feynman diagrams

TL;DR

This paper reviews recent advances in calculating multi-loop scattering amplitudes, emphasizing the development of causal integrand representations and a quantum algorithm for identifying causality-compatible flux configurations.

Contribution

It introduces a method to reconstruct integrand representations with only physical singularities and presents a quantum algorithm for detecting causality-compatible flux orientations.

Findings

Causal representations can be derived from binary partitions of Feynman diagrams.

A quantum algorithm effectively identifies flux configurations consistent with causality.

The approach improves the efficiency of multi-loop amplitude calculations.

Abstract

In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand level representation of scattering amplitudes which only contains physical singularities. These so-called causal representations can be derived from connected binary partitions of Feynman diagrams, properly entangled according to specific rules. We will focus on the detection of flux orientations which are compatible with causality, describing the implementation of a quantum algorithm to identify such configurations.