A Liouville-space method for the decoupling of the polarization propagator equation of motion

Statistical ensemble averages based on Liouville space matrix elements are used to introduce an alternative approach to the decoupling of the polarization propagator equation of motion. To this end, an appropriate ansatz for the (energy) propagator is introduced in the scenario of the superoperator algebra. The perturbation series which arises from the iteration of the (energy) Green function hierarchy allows, upon further expansion of the inverse of such series, to get the lower-order corrections to the Dyson self-energies. This procedure does not require inner projection of the superoperator resolvent or renormalization theory.