The spin-polarized homogeneous electron gas with densities Οββ
and Οββ for electrons with spin `up' (β) and spin `down'
(β), respectively, is systematically analyzed with respect to its
lowest-order reduced densities and density matrices and their mutual relations.
The three 2-body reduced density matrices Ξ³βββ,
Ξ³βββ, Ξ³aβ are 4-point functions for electron
pairs with spins ββ, ββ, and antiparallel,
respectively. From them, three functions Gβββ(x,y),
Gβββ(x,y), Gaβ(x,y), depending on only two variables,
are derived. These functions contain not only the pair densities but also the
1-body reduced density matrices. The contraction properties of the 2-body
reduced density matrices lead to three sum rules to be obeyed by the three key
functions Gssβ, Gaβ. These contraction sum rules contain corresponding
normalization sum rules as special cases. The momentum distributions
nββ(k) and nββ(k), following from fββ(r) and
fββ(r) by Fourier transform, are correctly normalized through
fsβ(0)=1. In addition to the non-negativity conditions
nsβ(k),gssβ(r),gaβ(r)β₯0 [these quantities are probabilities], it holds
nsβ(k)β€1 and gssβ(0)=0 due to the Pauli principle and gaβ(0)β€1
due to the Coulomb repulsion. Recent parametrizations of the pair densities of
the spin-unpolarized homogeneous electron gas in terms of 2-body wave functions
(geminals) and corresponding occupancies are generalized (i) to the
spin-polarized case and (ii) to the 2-body reduced density matrix giving thus
its spectral resolutions.Comment: 32 pages, 4 figure