Amplituhedron
Overview
A geometric object whose volume encodes scattering amplitudes in N=4 super Yang–Mills. Arkani-Hamed and Trnka (2013) showed that amplitudes emerge from the geometry without explicit Feynman diagrams.
Era: 2013
Proposed at: Princeton, USA (IAS)
Formal structure
Domain: Grassmannian Gr(k,n); momentum twistors Z_i ∈ ℂ⁴
A_n = ∫_{Γ} Ω_n; volume form on positive Grassmannian; Ω_n = ∏ d(log form)
Constraints: Positive region: positive coordinates; canonical form
Objective: Scattering amplitude = volume; no Feynman diagrams