Automatic calculation of Feynman loop-diagrams I. Generation of a simplified form of the amplitude

Abstract
In order to develop an automatic system to calculate loop diagrams in renormalizable theories, we present the first part of a complete system written in REDUCE and RLISP. It can generate the tensor and gamma matrix basis which is able to cast the total amplitude into a simpler form with the help of gauge invariance and symmetry among identical particles.

Title of program: FDC1
Catalogue Id: ACNY_v1_0

Nature of problem
In perturbative field theory, calculation of Feynman loop-process become more and more complicated and tedious as higher order correction is taken into account. Therefore, to develop programs to perform the work automatically become very useful. To construct a practicable program, there are many obstacles, such as how to express total amplitude to obtain the amplitude square, Feynman parameter integration, etc.

Versions of this program held in the CPC repository in Mendeley Data
ACNY_v1_0; FDC1; 10.1016/0010-4655(93)90010-A

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要
为开发一套可在可重整化理论（renormalizable theories）中计算圈图的自动化系统，本文展示了一套基于REDUCE与RLISP编写的完整系统的第一部分。该系统能够生成张量（tensor）与γ矩阵（gamma matrix）基矢，借助规范不变性（gauge invariance）与全同粒子（identical particles）间的对称性，可将总振幅（total amplitude）化简为更简洁的形式。

程序名称：FDC1
目录编号：ACNY_v1_0

问题概述
在微扰场论（perturbative field theory）中，随着高阶修正（higher order correction）的纳入，费曼圈过程（Feynman loop-process）的计算会愈发复杂繁琐。因此，开发自动完成此类计算的程序具有重要实用价值。若要构建实用的程序，则需克服诸多障碍，例如如何表示总振幅以得到振幅平方（amplitude square）、费曼参数积分（Feynman parameter integration）等问题。

Mendeley数据的CPC库中收录的本程序版本：ACNY_v1_0；FDC1；10.1016/0010-4655(93)90010-A

本程序源自贝尔法斯特女王大学（1969-2019年）维护的CPC程序库。