安徽大学学报（自然科学版）2025，Vol.49Issue(1)：8-18,11.DOI:10.3969/j.issn.1000-2162.2025.01.002
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
摘要
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分类
数理科学引用本文复制引用
张玉贤,冯晓丽,黄志祥,冯乃星..狄拉克矩阵在超复数系下的关联性[J].安徽大学学报（自然科学版）,2025,49(1):8-18,11.基金项目
国家自然科学基金资助项目(62101333,62271001) （62101333,62271001）
安徽省高等学校省级质量工程项目(2022xnjys007) （2022xnjys007）
