# University of Hertfordshire

## The hypersimplex canonical forms and the momentum amplituhedron-like logarithmic forms

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### Documents

Original language English 24 Journal of Physics A: Mathematical and Theoretical 30 Mar 2022 https://doi.org/10.1088/1751-8121/ac62ba E-pub ahead of print - 30 Mar 2022

### Abstract

In this paper, we provide a formula for the canonical differential form of the hypersimplex $\Delta_{k,n}$ for all $n$ and $k$. We also study the generalization of the momentum amplituhedron $\mathcal{M}_{n,k}$ to $m=2$, and we conclude that the existing definition does not possess the desired properties. Nevertheless, we find interesting momentum amplituhedron-like logarithmic differential forms in the $m=2$ version of the spinor helicity space, that have the same singularity structure as the hypersimplex canonical forms.