$Apart: A generalized Mathematica Apart function

Abstract We have generalized the Mathematica function Apart from 1 to N dimensions: the generalized function $Apart can decompose any linear dependent elements in Vx* to irreducible ones. The elements in Vx* can be viewed as the corresponding propagators which involve loop momenta, and the decomposition will be useful when one tries to perform loop calculations using packages such as Fire and Reduze, which have implemented the integration by parts (IBP) identities and Lorentz invariance (LI) identitie... Title of program: $Apart Catalogue Id: AEMK_v1_0 Nature of problem The traditional method of computing cross sections for a physical process in perturbative quantum field theory involves generating the amplitudes via Feynman diagrams and performing the dimensionally regularized loop integrals [1]. Simplifications of the expressions are performed at the analytical level, there an essential part is the reduction of these loop integrals to a small number of standard integrals. This step can be performed at the amplitude level for tensor integrals or, after contrac ... Versions of this program held in the CPC repository in Mendeley Data AEMK_v1_0; $Apart; 10.1016/j.cpc.2012.03.025 AEMK_v2_0; APart 2.0; 10.1016/j.cpc.2015.09.012 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)摘要 我们将Mathematica内置的Apart函数从1维推广至N维：推广后的$Apart函数可将Vx*空间内的任意线性相关元素分解为不可约形式。Vx*中的元素可视为包含圈动量的对应传播子，当使用者借助已实现分部积分（IBP）恒等式与洛伦兹不变性（LI）恒等式的工具包（如Fire与Reduze）开展圈计算时，该分解方法将具备重要应用价值。 程序名称：$Apart 目录编号：AEMK_v1_0 问题本质 微扰量子场论中计算物理过程截面的传统方法，是通过费曼图生成振幅并开展维度正规化圈积分计算[1]。需在解析层面完成表达式化简，其中核心环节之一是将这些圈积分约化为少量标准积分形式。该步骤可针对张量积分在振幅层面完成，或在收缩操作之后…… 本程序在Mendeley数据的CPC程序库中存有以下版本： AEMK_v1_0; $Apart; 10.1016/j.cpc.2012.03.025 AEMK_v2_0; APart 2.0; 10.1016/j.cpc.2015.09.012 本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2018）