Green's functions for composite fermions

In a regular fermionic system (such as a Fermi liquid), the Green’s function is given by

$$ G({bf k},,omega)=frac{1}{omega-epsilon_k-Sigma-idelta}$$

where $Sigma$ is the fermionic self-energy. My question is can we write the Green’s functions for composite fermions at arbitrary filling factor $nu$ in a similar fashion? Would it take the above form, but the self energy take on some non-trivial value? I’ve tried to survey the literature, and I could not find anything useful. Any explanation or contemporary papers that answer the previous questions would be greatly appreciated.