狄拉克矩阵在超复数系下的关联性
Associated characteristics of dirac matrices in the field of hyper-complex numbers
张玉贤 1冯晓丽 1黄志祥 1冯乃星1
作者信息
- 1. 安徽大学电子信息工程学院,信息材料与智能感知安徽省实验室,安徽 合肥 230601
- 折叠
摘要
在超复数系下,重点研究狄拉克矩阵的导出以及其固有的关联性,通过计算机来进行数值验证.先从超复数中的四元数定义出发,结合实虚矩阵的表达方式,给出一种获取狄拉克矩阵的广义表示方法.基于对四元数情况下的狄拉克矩阵进行重点研究分析,给出一组实矩阵与超复数系的对应关系,探索性地对超复数系中的其他情形给予定性研究.通过二元数、八元数以及十六元数等情形的计算实例,进一步验证狄拉克矩阵在超复数系下关联性的可行性和准确性.
Abstract
In the field of hyper-complex numbers,this article focused on the derivation of Dirac matrices and their inherent relevances,which were numerically validated through computers.This article started with the definition of quaternions in hyper-complex numbers and combined the representation of real and imaginary matrices to provide a generalized method for obtaining Dirac matrices.Afterwards,we focused on researching and analyzing the Dirac matrix in the case of quaternions,provided a set of correspondence between real matrices and hyper-complex systems,and explored qualitative research steps for other situations in the field of hyper-complex numbers.We further validated the feasibility and accuracy of studying the relevances of Dirac matrices in the field of hyper-complex numbers through computational examples of double-element numbers,octonion,and sedenion.
关键词
超复数/狄拉克矩阵/广义表示方法/计算实例Key words
hyper-complex numbers/Dirac matrices/generalized representation method/computational examples引用本文复制引用
出版年
2025
国家科技期刊平台
NSTL
万方数据