Self-energy corrections within the Composite Operator Method

The possibility to match the projection technique at the basis of the Composite Operator Method and the determination of the residual self-energy through the mode-coupling approximation is explored. The natural irreducibility given by the projection procedure is fully preserved and exploited. The expressions of the higher order propagators, within the mode-coupling approximation, in terms of the basic fermionic and bosonic propagators is given. The self-energy for the spin and charge propagators is computed in terms of convolutions of electronic propagators.