Radial quadratic oscillation defect in two dimensions
= Radial quadratic oscillation defect in two dimensions
{title2=$2\delta(|x|^2-a)-\pi\cos(ma)\delta_0$}
For $a>0$, polar-coordinate reduction and <integration by parts> give $m\sin(m||x|^2-a|)=2\delta(|x|^2-a)-\pi\cos(ma)\delta_0+o_{\mathcal D'}(1)$ in two dimensions. The circle term comes from the cusp in the folded phase, while the origin term is a radial endpoint contribution. A punctured-domain limit therefore need not extend across the quadratic critical point.