Abstract We present FeynCalc 9.3, a new stable version of a powerful and versatile Mathematica package for symbolic quantum field theory (QFT) calculations. Some interesting new features such as highly improved interoperability with other packages, automatic extraction of the ultraviolet divergent parts of 1-loop integrals, support for amplitudes with Majorana fermions and γ -matrices with explicit Dirac indices are explained in detail. Furthermore, we discuss some common problems and misunderstandings that may arise in the daily usage of the package, providing explanations and workarounds. Program summary Program Title: FeynCalc CPC Library link to program files: http://dx.doi.org/10.17632/cmpjr5ktmp.2 Licensing provisions: GNU GPLv3 Programming language: Wolfram Mathematica 8 and higher External routines/libraries: FeynArts [1] Journal reference of previous version: Comput. Phys. Commun., 207, 432–444, (2016). Does the new version supersede the previous version?: Yes Nature of problem: Symbolic calculation of Feynman diagrams in particle physics and suitable standalone expressions in Quantum Field Theory. Solution method: The required algorithms and algebraic identities are implemented in Wolfram Mathematica. Reasons for the new version: Highly improved interoperability with other packages, new routines for Dirac algebra and loop integral evaluation. Summary of revisions: FeynCalc can be loaded with arbitrary packages into the same Mathematica kernel without causing shadowing issues. Algebraic manipulations of Dirac matrices and spinors with explicit Dirac indices are now available. Amplitudes involving Majorana fermions (both written by hand or obtained with FeynArts [1] can be evaluated out-of-the box. The same goes for FeynArts -generated diagrams with 4-fermion operators. The algorithm of [2] is added to extract UV-poles from scalar 1-loop integrals (Passarino–Veltman functions) with an arbitrary number of external legs. Restrictions: In the case of multi-particle (beyond 1 → 3 and 2 → 3 ) or multiloop processes, it is not advisable to perform all algebraic evaluations only with FeynCalc and Mathematica . References [1] T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140, 418 (2001), arXiv:hep-ph/0012260 . [2] G. Sulyok, A closed expression for the UV-divergent parts of one-loop tensor integrals in dimensional regularization, Phys. Part. Nucl. Lett. 14, 631 (2017), arXiv:hep-ph/0609282 .

中文翻译：

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FeynCalc 9.3：新功能和改进

摘要 我们提出 FeynCalc 9.3，这是一个用于符号量子场论 (QFT) 计算的强大且通用的 Mathematica 软件包的新稳定版本。详细解释了一些有趣的新功能，例如与其他软件包的高度改进的互操作性、自动提取 1 环积分的紫外发散部分、支持具有 Majorana 费米子的幅度和具有显式狄拉克指数的 γ 矩阵。此外，我们还讨论了在日常使用包中可能出现的一些常见问题和误解，提供了解释和解决方法。程序摘要 程序名称：FeynCalc CPC 库程序文件链接：http://dx.doi.org/10.17632/cmpjr5ktmp.2 许可条款：GNU GPLv3 编程语言：Wolfram Mathematica 8 及更高版本 外部例程/库：FeynArts [1] 之前版本的期刊参考：Comput。物理。社区，207, 432–444, (2016)。新版本是否取代了以前的版本？：是 问题性质：粒子物理学中费曼图的符号计算和量子场论中合适的独立表达式。求解方法：所需的算法和代数恒等式在 Wolfram Mathematica 中实现。新版本的原因：高度改进与其他包的互操作性，狄拉克代数和循环积分评估的新例程。修订摘要：FeynCalc 可以与任意包一起加载到同一个 Mathematica 内核中，而不会导致阴影问题。现在可以使用显式狄拉克指数对狄拉克矩阵和旋量进行代数运算。