Covariantizing Phase Space

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.

6 pages, 1 figure; v2: PRD version, extended discussion of IRC safe and additive observables from Stokes' theorem

References in corpus (5)

• An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC
• A novel subtraction scheme for double-real radiation at NNLO
• New Angles on Energy Correlation Functions
• The Hidden Geometry of Particle Collisions
• Conformal-helicity duality & the Hilbert space of free CFTs

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