标题： 逐环巴伊科夫表示——策略与实现 显示英文标题

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

摘要： 在本文中，我们讨论费曼积分的Baikov表示法及其标准形式和逐环形式。 Baikov表示法是一种参数表示法，其显著特点是积分变量是费曼积分的传播子。 对于逐环形式的Baikov表示法，我们详细讨论了一种策略，以如何进行最优参数化，这种参数化能够使对于给定的费曼积分必须引入的额外积分变量数量最小。 此外，我们提出了一种名为BaikovPackage的Mathematica实现，该实现能够生成标准形式和逐环形式的Baikov表示法。 我们还讨论了一些关于Baikov表示法的细微之处和未解问题。 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.