Nima Arkani-Hamed, Jaroslav Trnka
2013 · arXiv
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.
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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 described in this paper: https://arxiv.org/abs/1312.2007
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 simplifying complex particle interactions, from tens of pages of Feynman diagrams to around a page. I think of the above as an extension of that project. However, I don't recall all the details, as it's been six years since I went to his talk on this.
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
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