arXiv 2102.015762021-02-02hep-phhep-th

交理论在Feynman积分中的应用：单变量情形

On the Application of Intersection Theory to Feynman Integrals: The Univariate Case

Hjalte Frellesvig, Luca Mattiazzi

备注：: Contribution to the proceedings of MathemAmplitudes 2019. 10 pages and three figures

摘要：

本文档是对2019年12月在意大利帕多瓦举行的MathemaAmplitude 2019会议的贡献。现代高能物理散射振幅计算中的一个关键步骤是利用线性关系将散射振幅表示为最小费曼积分集。在这项工作中，我们提出了一种创新的方法，基于交集理论，以实现这种分解。这允许直接计算缩减，以与向量可以被投影到向量基上相同的方式将出现在散射振幅中的积分投影到积分基上。具体地说，我们将推导和讨论最大割费曼积分之间的几个恒等式，展示它们的直接分解。这一贡献将集中在单变量的故事的一部分，与多元的概括正在讨论的不同贡献的加斯帕罗托和曼达尔。

英文摘要：

This document is a contribution to the proceedings of the MathemAmplitudes 2019 conference held in December 2019 in Padova, Italy. A key step in modern high energy physics scattering amplitudes computation is to express the latter in terms of a minimal set of Feynman integrals using linear relations. In this work we present an innovative approach based on intersection theory, in order to achieve this decomposition. This allows for the direct computation of the reduction, projecting integrals appearing in the scattering amplitudes onto an integral basis in the same fashion as vectors may be projected onto a vector basis. Specifically, we will derive and discuss few identities between maximally cut Feynman integrals, showing their direct decomposition. This contribution will focus on the univariate part of the story, with the multivariate generalisation being discussed in a different contribution by Gasparotto and Mandal.

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