标题： IBPs 和参数空间中的微分方程 显示英文标题

标题： IBPs and differential equations in parameter space

摘要： 我们提出了一种投影框架，用于构建费曼积分的分部积分（IBP）恒等式和微分方程，在费曼参数空间中进行操作。该框架源于早期的结果，这些结果在现代环计算技术发展之前就已经出现。通过将这些结果适应并推广到现代语言，我们使用射影几何的简单工具，在参数空间中生成一组IBP恒等式和微分方程，该技术适用于任何环序。我们在一环和两环的简单图上测试了该方法的可行性，并提供了对几个现有结果的统一观点。 显示英文摘要

摘要： We present a projective framework for the construction of Integration by Parts (IBP) identities and differential equations for Feynman integrals, working in Feynman-parameter space. This framework originates with very early results which emerged long before modern techniques for loop calculations were developed. Adapting and generalising these results to the modern language, we use simple tools of projective geometry to generate sets of IBP identities and differential equations in parameter space, with a technique applicable to any loop order. We test the viability of the method on simple diagrams at one and two loops, providing a unified viewpoint on several existing results.