论文标题
从壳上空间的几何形状上对连续不连续性的限制
Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
论文作者
论文摘要
我们介绍了超越斯坦曼关系的Feynman积分不连续性的几类约束。这些约束源于Pham提倡的Landau方程的几何公式，其中Feynman积分的奇异性对应于壳上空间之间地图的临界点。为了建立我们的结果，我们回顾了Picard-Lefschetz理论的元素，该理论将复杂的外部动量空间的同质属性与内部内部和外部动量的合并空间的同源性联系在一起。从该分析中出现的一个重要概念是一个问题是，是否可以同时满足这两个奇异性的兰道方程，是否兼容一对landau奇异性。在我们描述的条件下，相对于不兼容的Landau奇异性的顺序不连续性必须消失。尽管在本文中，我们只能严格证明Feynman积分与通用质量的结果，但我们期望我们获得的几何和代数见解也将有助于分析更一般的Feynman积分。
We present several classes of constraints on the discontinuities of Feynman integrals that go beyond the Steinmann relations. These constraints follow from a geometric formulation of the Landau equations that was advocated by Pham, in which the singularities of Feynman integrals correspond to critical points of maps between on-shell spaces. To establish our results, we review elements of Picard-Lefschetz theory, which connect the homotopy properties of the space of complexified external momenta to the homology of the combined space of on-shell internal and external momenta. An important concept that emerges from this analysis is the question of whether or not a pair of Landau singularities is compatible-namely, whether or not the Landau equations for the two singularities can be satisfied simultaneously. Under conditions we describe, sequential discontinuities with respect to non-compatible Landau singularities must vanish. Although we only rigorously prove results for Feynman integrals with generic masses in this paper, we expect the geometric and algebraic insights that we gain will also assist in the analysis of more general Feynman integrals.
