论文标题
Feynman积分的分解由多元交集数字
Decomposition of Feynman Integrals by Multivariate Intersection Numbers
论文作者
论文摘要
我们介绍了Feynman积分直接分解为预测主积分的基础的最新想法的详细描述，以及采用多元交叉数字的主积分满足的微分方程的直接派生。我们讨论了用于计算多元相交数量的递归算法，并为Feynman积分的直接分解提供了三种不同的方法，我们将直接分解，自下而上的分解和自上而下的分解配音。这些算法通过计算在各种订单中支持的相交数来利用Feynman积分的单位性结构，从而显示了与基于单位性的方法和积分分解的相交理论概念的合成。我们执行明确的计算，以举例说明应用于Feynman积分的所有这些方法，为通用多环积分的潜在应用铺平了道路。
We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master integrals, employing multivariate intersection numbers. We discuss a recursive algorithm for the computation of multivariate intersection numbers and provide three different approaches for a direct decomposition of Feynman integrals, which we dub the straight decomposition, the bottom-up decomposition, and the top-down decomposition. These algorithms exploit the unitarity structure of Feynman integrals by computing intersection numbers supported on cuts, in various orders, thus showing the synthesis of the intersection-theory concepts with unitarity-based methods and integrand decomposition. We perform explicit computations to exemplify all of these approaches applied to Feynman integrals, paving a way towards potential applications to generic multi-loop integrals.
