Expansion of the Density Matrix of an N-Fermion System in Terms of the Correlation Densities of Fermion Clusters

The N‐fermion density operator D = |Ψ〈〉Ψ| is decomposed into the densities of clusters of correlating fermions. The m‐body cluster densities ${\mathrm{\gamma ̂}}^{\mathrm{(m)}}$ are ``orthogonal'' to the one‐body ``Fock‐Dirac''‐type densities ρ₁, i.e., $\Gamma {\mathrm{r}}_1{\mathrm{(\rho }}_1{\mathrm{\gamma ̂}}_{\text{1,2,}}^{\mathrm{(m)}}{\dots }_{\mathrm{,m}}\text{)=0.}$ The reduced‐correlation‐density matrices obtained differ from the conventional reduced‐density‐matrices and are particularly convenient for the treatment of fermion‐fermion correlations.