标题： 逐环Baikov表示——策略与实现 显示英文标题

标题： The Loop-by-Loop Baikov Representation -- Strategies and Implementation

摘要： 本文中，我们讨论费曼积分的Baikov表示及其标准形式和逐圈形式。 Baikov表示是一种参数化表示，其定义特征在于积分变量是费曼积分的传播子。 对于逐圈Baikov表示，我们详细讨论了一种最优参数化的策略，这种参数化旨在最小化为给定费曼积分必须引入的额外积分变量的数量。 此外，我们还展示了一个名为BaikovPackage的Mathematica实现，它能够生成Baikov表示的标准形式和逐圈形式。 我们还讨论了关于Baikov表示的一些细节问题和尚未解决的问题。 显示英文摘要

摘要： In this paper, we discuss the Baikov representation of Feynman integrals in its standard and loop-by-loop variants. The Baikov representation is a parametric representation, which has as its defining feature the fact that the integration variables are the propagators of the Feynman integral. For the loop-by-loop Baikov representation, we discuss in detail a strategy for how to make an optimal parametrization which is one that minimizes the number of extra integration variables that have to be introduced for a given Feynman integral. Furthermore, we present a Mathematica implementation, named BaikovPackage, that is able to generate the Baikov representation in its standard and loop-by-loop varieties. We also discuss some subtleties and open problems regarding Baikov representations.