In planar N = 4 supersymmetric Yang–Mills theory, an amplituhedron is defined as a mathematical space known as the Positive Grassmannian.
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In the approach, the on-shell scattering process "tree" is described by a positive Grassmannian, a structure in algebraic geometry analogous to a convex polytope, that generalizes the idea of a simplex in projective space.
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Using Twistor theory, BCFW recursion relations involved in the scattering process may be represented as a small number of Twistor diagrams.