\sum_{n,m}\left[W(f,f,0,0)\hat{a}^\dagger_{n,f}\hat{a}_{n,f}\hat{a}^\dagger_{m,0}\hat{a}_{m,0}+W(f,0,f,0)\hat{a}^\dagger_{n,f}\hat{a}_{n,0}\hat{a}^\dagger_{m,f}\hat{a}_{m,0}+W(f,0,0f)...+...\right]