无三角剖分多面体的剖分
Volumes of Polytopes Without Triangulations
摘要：
对偶振幅面体的几何形状通常参考特定的三角测量来描述。一个给定的三角测量只显示了底层空间的某些方面，而掩盖了其他方面，因此理解这种几何形状而不参考特定的三角测量是可取的。本文介绍了一种新的计算任意维一般多面体体积的形式。我们定义了新的“顶点对象”，并介绍了一个演算表达量的多面体在他们。这些表达式是唯一的，独立于任何三角剖分，显然只依赖于底层多面体的顶点，并可以用来很容易地获得不同的三角剖分之间的身份。作为这种形式主义的一个应用，我们得到了新的表达式的体积的树级，$n$点NMHV双振幅面体。
英文摘要：
The geometry of the dual amplituhedron is generally described in reference to a particular triangulation. A given triangulation manifests only certain aspects of the underlying space while obscuring others, therefore understanding this geometry without reference to a particular triangulation is desirable. In this note we introduce a new formalism for computing the volumes of general polytopes in any dimension. We define new "vertex objects" and introduce a calculus for expressing volumes of polytopes in terms of them. These expressions are unique, independent of any triangulation, manifestly depend only on the vertices of the underlying polytope, and can be used to easily derive identities amongst different triangulations. As one application of this formalism, we obtain new expressions for the volume of the tree-level, $n$-point NMHV dual amplituhedron.
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