Diagram technique for the Anderson model

A temperature diagram technique is developed for calculating the Green's function of the operators of changing atomic configurations. Because Wick's theorem does not hold for the mean values of these operators, an expansion in semi-invariants is used Instead of the standard diagram technique. The formaIism is used to find the Green's function of the admixture $d$-electron in the Anderson model. It is shown that in the case when one of the admixture levels is near the Fermi surface summation of the Ieading diagrams in the logarithmic approximation is equivalent to decoupling of the two-time Green's functions and reduces to a renormalization of the admixture level.