 \hawk \sloth \dolphin \duck \pig\starfish\anteater \widetilde{f}(k_{1},k_{2})=2\pi |\theta^{12}|\ % \mathrm{Tr}_{\mathcal{H}}\left( \widehat{V}^{\dagger}(k_{1},k_{2})  \widehat{\mathcal{O}}_{f}(\hat{x}^{1},\hat{x}^{2})\right)~.  \label{eq:trvv}