   \delta\left(     \left|        \varepsilon_{\bf k} - \varepsilon_{({\bf k}+{\bf q})}     \right|     + \omega_{\bf q} - \lambda   \right)     \frac{     \left| g_{\bf q} \right|^{0}     \Theta\left[       \omega_{\bf q} -        \left| \varepsilon_{\bf k} - \varepsilon_{({\bf k}+{\bf q})} \right|     \right]   }{     \left|       \varepsilon_{\bf k} - \varepsilon_{({\bf k}+{\bf q})}      \right| + \omega_{\bf q}   }   \left\langle     c_{-({\bf k}+{\bf q}),\downarrow} c_{({\bf k}+{\bf q}),\uparrow}   \right\rangle,\