标题： 费曼积分的对偶，2：广义幺正性 显示英文标题

标题： Duals of Feynman Integrals, 2: Generalized Unitarity

摘要： 本系列的第一篇论文介绍了对象（扭相对上同调的元素），这些对象与费曼积分是对偶的。 我们展示了如何使用这些空间之间的配对——一种称为交数的代数不变量——来表达散射振幅，从而绕过生成积分约化恒等式的过程。 初始信息是在各种拓扑结构的切割上的被积函数，这些可以计算为内部树状图的乘积，提供了一种系统的方法来处理广义幺正性。 我们给出了两种计算多变量交数的算法。 作为第一个例子，我们计算了四点和五点胶子振幅在一般时空维度的情况。 我们也检查了我们形式主义的四维极限，并提供了提取有理项的处方。 显示英文摘要

摘要： The first paper of this series introduced objects (elements of twisted relative cohomology) that are Poincar\'e dual to Feynman integrals. We show how to use the pairing between these spaces -- an algebraic invariant called the intersection number -- to express a scattering amplitude over a minimal basis of integrals, bypassing the generation of integration-by-parts identities. The initial information is the integrand on cuts of various topologies, computable as products of on-shell trees, providing a systematic approach to generalized unitarity. We give two algorithms for computing the multi-variate intersection number. As a first example, we compute 4- and 5-point gluon amplitudes in generic spacetime dimension. We also examine the 4-dimensional limit of our formalism and provide prescriptions for extracting rational terms.