• 论文 •

### 由反对称化操作探究Levi-Civita与Kronecker符号的性质

1. 1.贵州师范大学物理与电子科学学院，贵州 贵阳 550001；
2. 贵州省射电天文数据处理重点实验室，贵州 贵阳 550001
• 收稿日期:2018-08-25 出版日期:2019-09-25 发布日期:2019-09-25

### Exploring the properties of Levi-Civita and Kronecker symbols through antisymmetrization

PENG Junjin1,2, LEI Liangjian1

1. 1. School of Physics and Electronic Science，Guizhou Normal University，Guiyang 550001，China)
2. Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing, Guiyang 550001，China
• Received:2018-08-25 Online:2019-09-25 Published:2019-09-25

Abstract:

In this paper, on basis of the determinant for the metric tensor, together with the identities got via anti-symmetrizing the Kronecker delta symbol and Levi-Civita tensor, we prove one of the properties of the Levi-Civita symbol (tensor), which shows that two Levi-Civita symbols (tensors) with the contraction for some or total indices can be expressed by a series of Kronecker delta symbols or the generalized Kronecker delta symbol. We further present two important deductions from the property of the Levi-Civita tensor, which are proved in other ways. Besides, we analyze several important properties for the generalized Kronecker delta symbol.