Semi-automatic calculations of multi-loop Feynman amplitudes with AmpRed

We present a Mathematica package AmpRed for the semi-automatic calculations of multi-loop Feynman amplitudes with high efficiency and precision. AmpRed implements the methods of integration by parts and differential equations in the Feynman-parameter representation. It allows for the calculations of general parametric integrals (which may not have momentum-space correspondences). Various user-friendly tools for multi-loop calculations, such as those to construct and solve differential equations for Feynman integrals, are provided. It can also deal with tensor algebras in non-relativistic field theories. Interfaces to some packages, like QGRAF and FORM, are also provided.我们研发了一款名为AmpRed的Mathematica软件包，可高效且精准地完成多圈费曼振幅（multi-loop Feynman amplitudes）的半自动计算。AmpRed基于费曼参数表示法（Feynman-parameter representation）实现了分部积分法与微分方程方法，支持计算一般参数积分（此类积分可能不存在动量空间对应形式）。软件包内置多款面向多圈计算的便捷工具，例如用于构建并求解费曼积分（Feynman integrals）微分方程的工具；其还可处理非相对论场论（non-relativistic field theories）中的张量代数（tensor algebras）问题，同时提供了与QGRAF、FORM等多款软件包的交互接口。