# How to calculate the Fock exchange interaction self-energy of a system in momenttum space

I have a Hamiltonian in the momentum space which has a strong non-local electron-electron interaction.

I know that I have to find its corresponding exchange self-energy and solve the Dyson equation self-consistently.

$$G = G_0 * \Sigma_I * G$$

which $$\Sigma$$ is a function of $$G$$. $$\quad$$ ($$\Sigma(G)$$)

So how does this self-energy look like in the momentum space. If there is not a specific self-energy, how should I start to make it step by step.