大学物理 ›› 2022, Vol. 41 ›› Issue (07): 51-.doi: 10.16854/j.cnki.1000-0712.210522

• 教学讨论 • 上一篇    下一篇

洛伦兹变换矩阵的对角化及其意义

李一杰,张成园,石  薇,康晓珅,龚  丽,许广智   

  1. 辽宁大学 物理学院,辽宁  沈阳110036
  • 收稿日期:2021-10-26 修回日期:2021-11-15 出版日期:2022-07-28 发布日期:2022-08-11
  • 通讯作者: 许广智,E-mail: xuguangzhi@lnu.edu.cn
  • 作者简介:李一杰(1985—),女,满族,辽宁锦州人,辽宁大学物理学院副教授,博士,主要从事粒子物理唯象学研究工作.
  • 基金资助:
    国家自然科学基金(11705078);辽宁大学本科教学改革研究项目(JG2020YBXM057; JG2020YBXM024; JG2020YBXM094; JG2018ZC72; JG2020KCSZ066)资助

Diagonalization of Lorentz transformation matrix and its significance

LI Yi-jie, ZHANG Cheng-yuan, SHI Wei, KANG Xiao-shen, GONG Li,  XU Guang-zhi   

  1. Department of Physics, Liaoning University, Shenyang, Liaoning 110036, China
  • Received:2021-10-26 Revised:2021-11-15 Online:2022-07-28 Published:2022-08-11

摘要: 通过对角化过程,讨论洛伦兹变换矩阵特征矢量、特征值的意义.将洛伦兹变换矩阵对角化,即将一般惯性参考系变换到光锥坐标系. 特征矢量是光锥坐标系坐标轴上的矢量. 特征值对应参考系变换下,光锥坐标分量的缩放大小. 本文可以帮助学生加深对洛伦兹变换及狭义相对论时空特性的理解.

关键词: 洛伦兹变换, 对角化, 光锥坐标系, 时空图

Abstract: The significance of eigenvectors and eigenvalues of Lorentz transformation matrix in the process of diagonalization are discussed. The procedure of diagonalizing Lorentz transformation matrix is to transform the general inertial frame of reference into the light-cone coordinate system. The eigenvectors are the vectors on the axis of light-cone coordinate system. The eigenvalues correspond to the scaling factor for the light-cone coordinate components under the reference frame transformation. This paper can help students to deepen their understanding of Lorentz transformation and the space-time characteristics of special relativity.

Key words: Lorentz transformation, diagonalization, light-cone coordinate system, time-space diagram