Positive Geometries in the Real World

Our understanding of the fundamental laws of Nature is based on the study of scattering amplitudes, traditionally computed using Feynman diagrams.In the past three decades, the shortcomings of this representation have become increasingly clear.

Scattering amplitudes enjoy a simplicity which is destroyed by Feynman diagrams, resulting in an overwhelming apparent complexity of computations.This has motivated the search for alternatives to Feynman diagrams, which culminated in the discovery that scattering amplitudes in two toy theories, maximally supersymmetric Yang-Mills theory, and the simplest theory describing colored scalars, can be computed as ""Volumes"" of positive geometries: regions in kinematic space carved out by inequalities.In the new representation it is the usual properties kept manifest by Feynman diagrams, Locality and Unitarity, which are now obscured while the simplicity of scattering amplitudes is restored.These developments are both conceptually intriguing and practically useful; however, they have so far been limited to applications in toy theories only.The goal of PositiveWorld (Positive geometries in the real World) is to address this issue, using the lessons learned in these examples to describe our world, thus marching towards a reformulation of physics completely alternative to the traditional language of Quantum Field Theory and Feynman diagrams.The guiding principle in this exploration is that progress is measured by the efficiency of computations.

Therefore, concrete results within PositiveWorld are presented in the form of novel algorithms to address calculations on various topics of scattering theory, with practical applications for theoretical predictions of experiments taking place at particle colliders.