论文标题
fieldsx- XACT张量计算机代数套件的扩展包，包括费米子，量规场和BRST共同体
FieldsX -- An extension package for the xAct tensor computer algebra suite to include fermions, gauge fields and BRST cohomology
论文作者
论文摘要
我介绍了张量计算机代数软件包fieldsx，它扩展了Tensor代数软件包的XACT套件，以使用费米和仪表字段进行现场理论中的计算。这包括弯曲空间$γ$矩阵的标准工具，fierz身份，lie代数上不变的张量，任意等级以及左右变分衍生物，以及旋转产品在不可舒服的组件中分解为D'Auria，fré，fré，bré，缅因州和雷格（Regge）[nental and regge and ners ynals phys [ennals ynals phys [ennals phys toss of。 139（1982）93]。最后，它还包括使用nilpotent差异的功能，例如（超对称）规格理论的BV-BRST差异，并计算其（相对）共同体，从中可以确定异常和规范的运算符。我以$ \ Mathcal {n} = 1 $ super-yang-mills理论的示例说明了包装的使用。
I present the tensor computer algebra package FieldsX, which extends the xAct suite of tensor algebra packages to perform computations in field theory with fermions and gauge fields. This includes the standard tools of curved-space $γ$ matrices, Fierz identities, invariant tensors on Lie algebras, arbitrary gradings and left and right variational derivatives, as well as the decomposition of spinor products into irreducible components following the approach of d'Auria, Fré, Maina and Regge [Annals Phys. 139 (1982) 93]. Lastly, it also includes functions to work with nilpotent differentials such as the BV-BRST differential for (supersymmetric) gauge theories and to compute their (relative) cohomologies, from which anomalies and gauge-invariant operators can be determined. I illustrate the use of the package with the example of $\mathcal{N}=1$ Super-Yang--Mills theory.
