论文标题
Amplituhedron的边界与Amplituhedronboundaries
Boundaries of the Amplituhedron with amplituhedronBoundaries
论文作者
论文摘要
积极的几何形状为计算各种物理模型的散射幅度提供了现代方法。为了促进对这些新几何方法的探索，我们介绍了一个数学包装，称为``amplituhedronboundaries''，用于计算三种积极几何形状的边界结构：amplituhedron $ \ nathcal $ \ mathcal {a} $ \ MATHCAL {M} _ {n，k}^{（m）} $和HyperSimplex $δ_{k，n} $。前两个几何形状与平面$ \ Mathcal {n} = 4 $ sym中的散射幅度有关，而最后一个是数学上许多情况下出现的良好的polytope，并且与$ \ Mathcal {M Mathcal {M} _ {n，k}^^^（2）$密切相关。该软件包包括一系列有用的工具，用于研究这些积极的几何形状，包括它们的边界分层，绘制其边界posets以及操纵组合结构的其他工具。
Positive geometries provide a modern approach for computing scattering amplitudes in a variety of physical models. In order to facilitate the exploration of these new geometric methods, we introduce a Mathematica package called ``amplituhedronBoundaries'' for calculating the boundary structures of three positive geometries: the amplituhedron $\mathcal{A}_{n,k}^{(m)}$, the momentum amplituhedron $\mathcal{M}_{n,k}^{(m)}$ and the hypersimplex $Δ_{k,n}$. The first two geometries are relevant for scattering amplitudes in planar $\mathcal{N}=4$ SYM, while the last one is a well-studied polytope appearing in many contexts in mathematics, and is closely related to $\mathcal{M}_{n,k}^{(2)}$. The package includes an array of useful tools for the study of these positive geometries, including their boundary stratifications, drawing their boundary posets, and additional tools for manipulating combinatorial structures useful for positive Grassmannians.
