First-order repair and the larger-support residual

For comparison with an expanded retarded formula, write ${\overline{H}}^{\mu \nu }=H^{\mu \nu }-\frac{1}{2}{\eta }^{\mu \nu }{\mathrm{tr}}_{\eta }H$. Then

Indeed, expand ${\mathcal{Q}}_{gK\xi }$, and use ${\mathsf{E}}_m{P}_m(g{X}_{\xi }{\varphi }_0)=g{X}_{\xi }{\varphi }_0$. This independently reproduces the classical mechanism compared with VI CheungVI.