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arXiv · 2402.06527

Adjoints and Canonical Forms of Tree Amplituhedra

Kristian Ranestad·Rainer Sinn·Simon Telen
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Abstract

We consider semi-algebraic subsets of the Grassmannian of lines in three-space called tree amplituhedra. These arise in the study of scattering amplitudes from particle physics. Our main result states that tree amplituhedra in ${\rm Gr}(2,4)$ are positive geometries. The numerator of their canonical form plays the role of the adjoint in Wachspress geometry, and is uniquely determined by explicit interpolation conditions.

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Kristian Ranestad, Rainer Sinn, Simon Telen. 2024-02-09. Adjoints and Canonical Forms of Tree Amplituhedra. https://doi.org/10.7146/math.scand.a-149816

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