The Amplituhedron
By N. Arkani-Hamed, J. Trnka. 2013
175 citations recorded by the source corpus.
A bstractPerturbative 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$$ \mathcal{N}=4 $$ 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.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ccdea53e60d12207a52a5825bd3e7601b31219d7
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Citations in the corpus
- Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions (2014, background): “It seems also propitious to look for connections between the OPE program and recent perturbative approaches such as the Integrand [42], the Positive Grassmanian [43], or the Amplituhedron [44].”
- The cosmological bootstrap: inflationary correlators from symmetries and singularities (2018, unknown): “Indeed, even some first hints for such a description, seen in perturbation theory, involve much more alien combinatorial, geometric and number-theoretic ideas [9–16], from which the physics of spacetime and quantum mechanics—locality and unitarity—emerge as derivative notions, with a huge amount lef”