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1. chinaXiv:202011.00118 [pdf]

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

宋义生; 祁力群
Subjects: Mathematics >> Mathematical Physics

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.

submitted time 2020-11-23 Hits3149Downloads457 Comment 0

2. chinaXiv:201911.00094 [pdf]

Copositivity for 3rd order symmetric tensors and applications

刘佳蕊; 宋义生
Subjects: Mathematics >> Mathematical Physics

The strict opositivity of 4th order symmetric tensor may apply to detect vacuum stability of general scalar potential. For finding analytical expressions of (strict) opositivity of 4th order symmetric tensor, we may reduce its order to 3rd order to better deal with it. So, it is provided that several analytically sufficient conditions for the copositivity of 3th order 2 dimensional (3 dimensional) symmetric tensors. Subsequently, applying these conclusions to 4th order tensors, the analytically sufficient conditions of copositivity are proved for 4th order 2 dimensional and 3 dimensional symmetric tensors. Finally, we apply these results to present analytical vacuum stability conditions for vacuum stability for $\mathbb{Z}_3$ scalar dark matter.

submitted time 2019-11-23 Hits19890Downloads1223 Comment 0

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