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# A necessary and su#14;cient condition of positive definiteness for 4th order symmetric tensors defined in particle physics

Submit Time: 2020-11-23
Author: 宋义生 1 ; 祁力群 2 ;
Institute: 1.重庆师范大学; 2.杭州电子科技大学;

## Abstracts

 In this paper, we mainly discuss analytical expressions of positive definiteness for a special 4th order 3-dimensional symmetric tensor defined by the constructed model for a physical phenomenon. Firstly, an analytically necessary and sufficient conditions of 4th order 2-dimensional symmetric tensors are given to test its positive definiteness. Furthermore, by means of such a result, a necessary and sufficient condition of positive definiteness is obtained for a special 4th order 3-dimensional symmetric tensor. Such an analytical conditions can be used for verifying the vacuum stability of general scalar potentials of two real singlet scalar fields and the Higgs boson. The positive semi-definiteness conclusions are presented too.
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From: 宋义生
DOI：10.12074/202011.00118
Recommended references： 宋义生,祁力群.(2020).A necessary and su#14;cient condition of positive definiteness for 4th order symmetric tensors defined in particle physics.[ChinaXiv:202011.00118] (Click&Copy)
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[V1] 2020-11-23 15:54:17 chinaXiv:202011.00118V1 Download
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