Radial and angular modes of an orthogonally invariant scalar potential
= Radial and angular modes of an orthogonally invariant scalar potential
{title2=$m_\eta^2=2\lambda v^2$}
For $V=m^2\phi^2/2+\lambda(\phi^2)^2/4$, $m^2<0$, the <vacuum manifold> is a sphere of radius $v=\sqrt{-m^2/\lambda}$. At a chosen vacuum the <Hessian matrix> is $2\lambda v^2nn^T$, where $n$ is its unit direction. The radial scalar has mass squared $2\lambda v^2$; the $n-1$ angular modes are physical <Goldstone bosons> when the symmetry is global.