Spontaneous symmetry breakdown and symmetric spaces

Spontaneous breakdown of a (compact) internal-symmetry group $G$ to a (unbroken) subgroup $H$ is analyzed using the procedure developed in a previous paper. It is found that the desired analysis can be carried through only if the pair ($G, H$) is such that the corresponding coset space $\frac{G}{H}$ is a symmetric space (a Riemannian globally symmetric space).