振幅面体与amplituhedronBoundaries的边界
Boundaries of the Amplituhedron with amplituhedronBoundaries
摘要：
正几何为计算各种物理模型中的散射振幅提供了一种现代方法。为了便于探索这些新的几何方法，我们引入了一个Mathematica软件包，称为“振幅边界”，用于计算三个正几何的边界结构：振幅面体$\mathcal{A}_{n,k}^{(m)}$，动量振幅面体$\mathcal{M}_{n,k}^{(m)}$和超单纯形$Δ_{k,n}$。前两种几何形状与平面$\mathcal{N}=4$ SYM中的散射振幅有关，而最后一种几何形状是在数学中的许多上下文中出现的经过充分研究的多面体，并且与$\mathcal{M}_{n,k}^{(2)}$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，包括他们的边界分层，绘制他们的边界偏序集，以及其他工具，用于操纵组合结构的积极格拉斯曼。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
