HackerPapers

arXiv:1312.2007hep-th

The Amplituhedron

Nima Arkani-Hamed, Jaroslav Trnka

Abstract

Perturbative scattering amplitudes in gauge theories have remarkable simplicity and hidden infinite dimensional symmetries that are completely obscured in the conventional formulation of field theory using Feynman diagrams. This suggests the existence of a new understanding for scattering amplitudes where locality and unitarity do not play a central role but are derived consequences from a different starting point. In this note we provide such an understanding for N=4 SYM scattering amplitudes in the planar limit, which we identify as ``the volume" of a new mathematical object--the Amplituhedron--generalizing the positive Grassmannian. Locality and unitarity emerge hand-in-hand from positive geometry.

arXiv comments
36 pages, 14 figures
Journal reference
DOI
doi:10.1007/JHEP10(2014)030
Subjects
hep-thHigh Energy Physics, Theory math.AGAlgebraic Geometry

On Hacker News

Linked by 3 identifiable commenters in 3 comments across 3 threads, from Feb 2019 to Oct 2022.

Comments linking this paper, per year.

Discussed in comments3 threads

  1. Nima Arkani-Hamed: The End of Space-Time [video] 1 comment

    • It's a popular science talk, not a presentation of a specific research result. The re-interpretation of scattering amplitudes in terms of novel mathematical structures is almost its own subfield of theoretical particle physics. Most of the specific results he mentioned are…

      cschmidView on HNParent context

  2. Gravity Is Not Like the Other Forces 1 comment

    • The 'Amplituhedron': https://arxiv.org/pdf/1312.2007.pdf The idea is to focus on the amplitude of scattering interactions from the momentum-space twistor perspective, rather than perturbations about a point in space-time. For background: Nima made a name for himself by greatly…

      RaroView on HNParent context

  3. Amplituhedron 1 comment

    • Glad you posted this but that article is a bit user-hostile even for math wikipedia. The relevant paper is relatively approachable if you're a mathematical tourist. https://arxiv.org/pdf/1312.2007.pdf

      anigbrowlView on HNParent context

Submitted to Hacker News

Connected through shared HN threads, not inferred similarity or a recommendation.