AI 中文总结
该研究推出Julia包Alakazam，用于场论与量子力学的张量表达式符号运算，具备多项关键功能且速度优于现有系统，可用于研究时空、超对称结构及后代、不变量等内容。
AI 中文摘要
我们推出「Alakazam」，这是一个用于场论和量子力学研究中产生的张量表达式符号运算的Julia包。它将成为研究时空与超对称结构的强大工具，包括支持超空间中的计算。该包实现了多项关键功能，如指标升降、哑指标项化简、替换模式、微分与变分演算、玻色与费米 grading、伽马矩阵恒等式以及李括号与对易子。我们展示了其相较于现有系统的显著速度提升，一些潜在应用包括后代与不变量的研究。
英文摘要
We present "Alakazam", a Julia package for performing symbolic manipulations of tensor expressions arising in the study of field theories and quantum mechanics. This will serve as a powerful tool for studying spacetime and supersymmetric structures, including support for calculations in superspace. The package implements many key features such as raising and lowering indices, simplification of terms with dummy indices, replacement patterns, differential and variational calculus, bosonic and fermionic grading, gamma matrix identities, and Lie brackets and commutators. We present notable speed improvements over established systems. Some possible applications include the study of descendants and invariants.
Comments130 pages, 15 figures, 9 tables; Julia demo scripts included, benchmarking scripts included
