Recursive generation of cartesian angular momentum coupling trees for SO(3)

Abstract Two computer algorithms are evaluated for the reduction of angular momentum coupling trees with vector (j = 1) terminals with a Cartesian choice of basis as used in nonlinear optics. Rather than employ advanced tensor algebra, both methods essentially iterate in distinct ways the basic techniques of angular momentum coupling. Turbo Pascal programs implementing these algorithms are presented and compared. The accompanying analysis integrates the Cartesian ten... Title of program: AMTREES Catalogue Id: ABRD_v1_0 Nature of problem When the geometry of a nonlinear optical experiment is altered, by changing the polarisation of one or more participating light beams or by space-time operations on the applied fields or the medium, the resulting change in the optical effect is restricted by symmetry considerations, and can be predicted from the knowlegde of a set of irreducible physical constants. As nonlinear optical processes of ever greater complexity become feasible and of interest, the construction of an efficient algorith ... Versions of this program held in the CPC repository in Mendeley Data ABRD_v1_0; AMTREES; 10.1016/0010-4655(90)90188-7 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

摘要 针对非线性光学（nonlinear optics）中采用笛卡尔基矢选择（Cartesian choice of basis）的矢量（角量子数j=1）端基角动量耦合树（angular momentum coupling tree）的约化问题，对两款计算机算法进行了评估。两款方法均未借助高级张量代数（advanced tensor algebra），而是通过不同方式迭代实现角动量耦合（angular momentum coupling）的基础技术。本文给出了实现这两种算法的Turbo Pascal程序并进行了对比分析。随附的分析整合了笛卡尔[原文未完整收尾]。
程序标题：AMTREES
目录编号：ABRD_v1_0
问题本质：当非线性光学（nonlinear optics）实验的几何构型发生改变时——例如调整一个或多个参与光束的偏振态，或对施加的场或介质执行时空操作——光学效应的变化会受到对称性约束，且可通过一组不可约物理常数（irreducible physical constants）的已知信息进行预测。随着复杂度不断提升的非线性光学（nonlinear optics）过程逐渐具备可行性并引发研究兴趣，构建高效算法的需求愈发迫切。
Mendeley数据的CPC程序库（CPC repository）中收录的该程序版本：ABRD_v1_0；AMTREES；10.1016/0010-4655(90)90188-7
本程序源自贝尔法斯特女王大学托管的CPC程序库（1969-2018年）