参数空间中的IBP与微分方程
IBPs and differential equations in parameter space
AI总结：
本研究提出一种在费曼参数空间中构建IBP恒等式与费曼积分微分方程的射影框架，将早期成果推广至现代语言，适用于任意圈阶，经单双圈简单图验证可行，为现有相关结果提供统一视角。
摘要：
我们提出了一种在费曼参数空间中构建分部积分（Integration by Parts，IBP）恒等式与费曼积分微分方程的射影框架。该框架源自远早于现代圈图计算技术发展的早期研究成果。我们将这些成果适配并推广至现代语言，利用射影几何的简单工具生成参数空间中的多组IBP恒等式与微分方程，该技术适用于任意圈阶。我们在单圈和双圈的简单图上测试了该方法的可行性，为若干现有结果提供了统一视角。
英文摘要：
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.
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