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.