Kira—A Feynman integral reduction program

In this article, we present a new implementation of the Laporta algorithm to reduce scalar multi-loop integrals appearing in quantum field theoretic calculations to a set of master integrals. We extend existing approaches by using an additional algorithm based on modular arithmetic to remove linearly dependent equations from the system of equations arising from integration-by-parts and Lorentz identities. Furthermore, the algebraic manipulations required in the back substitution are optimized. We describe in detail the implementation as well as the usage of the program. In addition, we show benchmarks for concrete examples and compare the performance to Reduze 2 and FIRE 5. In our benchmarks we find that Kira is highly competitive with these existing tools.本文提出一种全新的拉波塔（Laporta）算法实现方案，用于将量子场论计算中出现的标量多圈积分约化为一组主积分（master integrals）。本研究通过引入一种基于模算术（modular arithmetic）的附加算法，从分部积分（integration-by-parts）与洛伦兹恒等式（Lorentz identities）导出的方程组中剔除线性相关方程，以此拓展了现有研究方法。此外，本研究还对回代过程中所需的代数操作进行了优化。本文详细阐述了该程序的实现细节与使用方式。除此之外，本文通过具体实例展示了程序的基准测试结果，并将其性能与Reduze 2、FIRE 5两款现有工具进行了对比。经基准测试验证，Kira与上述现有工具相比具备极强的性能竞争力。