Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
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DOI：
10.1016/j.cpc.2017.09.014
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发表时间：
2017-05
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通讯作者：
C. Meyer
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作者：
C. Meyer
通过使用规范基可以极大地促进费曼积分微分方程的积分。本文介绍了 Mathematica 包 CANONICA，它实现了最近开发的算法来自动转换到规范基础。这代表了第一个适用于取决于多个尺度的微分方程的公开可用的实现。除了软件包的介绍之外，本文还扩展了算法某些方面的描述，包括规范形式直到常量变换的唯一性证明。 程序摘要 程序标题：CANONICAProgram Files doi：http://dx.doi.org/10.17632/fmwnmmhn77.1 许可规定：GNU 通用公共许可证版本 3 编程语言：Wolfram Mathematica，版本 10 或更高版本问题：计算主积分的有理基变换，得到相应微分方程的规范形式。解决方法：在维数调节器中扩展变换律。所得到的变换展开系数的微分方程用有理拟解法求解。
The integration of differential equations of Feynman integrals can be greatly facilitated by using a canonical basis. This paper presents the Mathematica packageCANONICA, which implements a recently developed algorithm to automatize the transformation to a canonical basis. This represents the first publicly available implementation suitable for differential equations depending on multiple scales. In addition to the presentation of the package, this paper extends the description of some aspects of the algorithm, including a proof of the uniqueness of canonical forms up to constant transformations.Program summaryProgram Title: CANONICAProgram Files doi:http://dx.doi.org/10.17632/fmwnmmhn77.1Licensing provisions:GNU General Public License version 3Programming language:Wolfram Mathematica, version 10 or higherNature of problem:Computation of a rational basis transformation of master integrals leading to a canonical form of the corresponding differential equation.Solution method:The transformation law is expanded in the dimensional regulator. The resulting differential equations for the expansion coefficients of the transformation are solved with a rational ansatz.