Vacuum stability conditions of the general two-Higgs-doublet potential

摘要: In this paper, we present how to calculate the bounded from below or the vacuum stability  of scalar potential for a general CP violating two-Higgs-doublet model  by using the concepts of co-positivity and the gauge orbit spaces.  Meanwhile, the semi-positive definiteness is prove for a class of 4th-order 2-dimensional complex tensor.