Balancing act: Multivariate rational reconstruction for IBP
Balancing act: Multivariate rational reconstruction for IBP
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DOI：
10.1016/j.nuclphysb.2023.116253
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发表时间：
2023-03
影响因子：
2.8
通讯作者：
A. V. Belitsky;A. V. Smirnov;R. Yakovlev
中科院分区：
文献类型：
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作者：
A. V. Belitsky;A. V. Smirnov;R. Yakovlev
我们解决的问题，明确重建的有理函数的许多变量。这对于基于模运算的逐部分积分恒等式（IBP）中的精确展开系数的恢复特别相关。这些IBP是必不可少的现代方法来评估多圈费曼积分的微分方程。当处理涉及大量洛伦兹不变量的高多重性情况时，模运算比代数实现要优越得多上级。我们介绍了一种新的方法，平衡关系的基础上，它允许一个以最少的数据输入，以实现一个强大的功能恢复的目标。该技术作为Mathematica packageReconstruction.min在FIRE6环境中实现，从而成功地证明了概念。
We address the problem of unambiguous reconstruction of rational functions of many variables. This is particularly relevant for recovery of exact expansion coefficients in integration-by-parts identites (IBPs) based on modular arithmetic. These IBPs are indispensable in modern approaches to evaluation of multiloop Feynman integrals by means of differential equations. Modular arithmetic is far more superior to algebraic implementations when one deals with high-multiplicity situations involving a large number of Lorentz invariants. We introduce a new method based on balanced relations which allows one to achieve the goal of a robust functional restoration with minimal data input. The technique is implemented as a Mathematica packageReconstruction.min the FIRE6 environment and thus successfully demonstrates a proof of concept.