Covariantizing Phase Space

TL;DR

This paper develops a covariant framework for phase space calculations, introducing geometric tools and new definitions that impact particle physics analysis methods and computational techniques.

Contribution

It presents a covariant approach to phase space, establishing Stokes' theorem, and introduces geometric structures relevant for high-dimensional particle physics applications.

Findings

Phase space is isomorphic to a product of a simplex and a hypersphere.

New definitions of infrared and collinear safety are provided.

Implications for subtraction schemes and machine learning in particle physics.

Abstract

We covariantize calculations over the manifold of phase space, establishing Stokes' theorem for differential cross sections and providing new definitions of familiar observable properties like infrared and collinear safety. Through the introduction of explicit coordinates and a metric we show phase space is isomorphic to the product space of a simplex and a hypersphere, and we identify geometric phenomena that occur when its dimensions are large. These results have implications for fixed order subtraction schemes, machine learning in particle physics and high-multiplicity heavy ion collisions.