    \mathcal{G}_{\tilde\rho\tilde\rho}({\mathrm{i}}\omega_0) \mathcal{G}_{\tilde\sigma\tilde\sigma}({\mathrm{i}}\omega_0) \delta({\mathrm{i}}\omega_0 + {\mathrm{i}}\omega_0 - {\mathrm{i}}\omega_0 - {\mathrm{i}}\omega_0)  