两个实标量场与希格斯玻色子的一般标量势的下有界条件
Boundedness from below conditions for a general scalar potential of two real scalars fields and the Higgs boson
AI总结：
本文针对两个实标量场与希格斯玻色子的一般标量势，通过将其转化为4阶3维对称张量的正定性问题，给出了解析的充分必要条件，从而解决了势函数下有界性的判定问题。
摘要：
两个实标量场与一个希格斯玻色子的最一般标量势是关于3个变量的四次齐次多项式，其定义了一个4阶3维对称张量。因此，这种标量势的下有界性涉及相应张量的正（半）定性。所以，本文主要讨论这种特殊的4阶3维对称张量的正（半）定性的解析表达式。首先，给出了一个解析的充分必要条件来检验4阶2维对称张量的正（半）定性。进一步，借助该结果，得到了两个实标量场与希格斯玻色子的一般标量势的下有界性的充分必要条件。
英文摘要：
The most general scalar potential of two real scalar fields and a Higgs boson is a quartic homogeneous polynomial about 3 variables, which defines a 4th order 3 dimensional symmetric tensor. Hence, the boundedness from below of such a scalar potential involves the positive (semi-)definiteness of the corresponding tensor. So, we mainly discuss analytical expressions of positive (semi-)definiteness for such a special 4th order 3-dimension symmetric tensor in this paper. Firstly, an analytically necessary and sufficient condition is given to test the positive (semi-)definiteness of a 4th order 2 dimensional symmetric tensor. Furthermore, by means of such a result, the necessary and sufficient conditions of the boundedness from below are obtained for a general scalar potential of two real scalar fields and the Higgs boson.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
