SO(3) invariant quartic scalar potential ($V=\frac{\lambda }{4}({\Phi }^T\Phi -v^2{)}^2$)

The scalar potential $V(\Phi )=\lambda ({\Phi }^T\Phi -v^2{)}^2/4$, with $\lambda >0$, is invariant under the SO(3) group. For $v>0$, its vacuum manifold is a sphere. Canonical scalar normalization gives radial mass squared $2\lambda v^2$.