The complete free Green matrix

Let ${{\mathsf{E}}_{\mathsf{m}}}^{\mathrm{R}/\mathrm{A}}$ be the Minkowski Green operators for $P_m$, and let ${{\mathsf{E}}_0}^{\mathrm{R}/\mathrm{A}}$ be those for $\square$. Their compact-source inverse identities and causal support are the ordinary Minkowski wave-theory inputs BGP.

The bosonic $r,b$ Hessian is