Lemma

In ${\mathcal{D}}^{\prime }(M)$, ${\partial }_{\mu }B=x_{\mu }R/2$.

Proof. Time differentiation gives $(8\pi {)}^{-1}{\int }_{{\mathbb{R}}^3}\psi (|\mathbf{x}|,\mathbf{x}){\mathrm{d}}^{3}x$. Spatial differentiation gives the same integral multiplied by $-x^i/|\mathbf{x}|$. These equal the actions of $tR/2$ and $x_{i}R/2$. The integrals are locally integrable at the vertex; there is no additional point mass.