论文标题
Baikov表示，交叉理论和规范的Feynman积分
Baikov representations, intersection theory, and canonical Feynman integrals
论文作者
论文摘要
规范微分方程的方法是计算量子字段理论中Feynman积分的重要工具。已经意识到，规范基础与$ d $ d $ d \ log $ - form-form intements密切相关。在这项工作中，我们介绍了逐环代表的广义循环概念，并使用相交理论的语言阐明了其与Feynman积分的关系和差异。然后，我们利用广义的baikov代表来构建$ d $ d $ d \ log $ - form-form intements，并讨论如何将它们转换为Feynman积分。我们描述了我们方法的技术细节，特别是如何处理施工程序中遇到的困难。我们的方法为查找Feynman积分的规范基础的问题提供了一种建设性的方法，我们证明了它适用于涉及多个物理尺度的复杂散射幅度。
The method of canonical differential equations is an important tool in the calculation of Feynman integrals in quantum field theories. It has been realized that the canonical bases are closely related to $d$-dimensional $d\log$-form integrands. In this work, we introduce the concept of generalized loop-by-loop Baikov representation, and clarify its relation and difference with Feynman integrals using the language of intersection theory. We then utilize the generalized Baikov representation to construct $d$-dimensional $d\log$-form integrands, and discuss how to convert them to Feynman integrals. We describe the technical details of our method, in particular how to deal with the difficulties encountered in the construction procedure. Our method provides a constructive approach to the problem of finding canonical bases of Feynman integrals, and we demonstrate its applicability to complicated scattering amplitudes involving multiple physical scales.
