当前位置: 首页 > 科学研究 > 学术交流 > 正文
学术交流

Analytical expressions of copositivity for 4th order symmetric tensors

2019-11-05 14:12

报告人: 宋义生

报告人单位: 河南师范大学

时间: 2019-11-09 11:00-12:00

地点: 北洋园校区32-B106

开始时间: 11:00

报告人简介: 教授

年: 2019

日月: 11.09

In particle physics, scalar potentials have to be bounded from below in order for the physics to make sense. The precise expressions of checking lower bound of scalar potentials are essential, which is an analytical expression of checking copositivity and positive definiteness of tensors given by such scalar potentials. Because the tensors given by general scalar potential are 4th order and symmetric, our work mainly focuses on finding precise expressions to test copositivity and positive definiteness of 4th order tensors in this paper. First of all, an analytically sufficient and necessary condition of positive definiteness is provided for 4th order 2 dimensional symmetric tensors. For 4th order 3 dimensional symmetric tensors, we give two analytically sufficient conditions of (strictly) cpositivity by using proof technique of reducing orders or dimensions of such a tensor. Furthermore, an analytically sufficient and necessary condition of copositivity is showed for 4th order 2 dimensional symmetric tensors. We also give several distinctly analytically sufficient conditions of (strict) copositivity for 4th order 2 dimensional symmetric tensors. Finally, we apply these results to check lower bound of scalar potentials, and to present analytical vacuum stability conditions for potentials of two real scalar fields and the Higgs boson.

联系我们

地址:天津市海河教育园区雅观路135号32号教学楼,300350
邮箱: maths@tju.edu.cn
电话:+86(0)22 27402850
传真:+86(0)22 27402850

扫码关注学院最新动态