Permutation-Algebraic Formulation of Spin-Free Transition Density Matrices

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Abstract
Spin‐free transition density matrices are derived from spin‐free kets which are symmetry‐adapted to the symmetric group and its algebra. The Dirac identity establishes that these spin‐free density matrices are identical to those obtained by integrating the spin from the full‐spin density martices. Derivations are first given for arbitrary primitive kets which may be geminals of higher polymals, after which we consider products of orbitals, either orthonormal or nonorthonormal. Correlation in the spin‐free space is discussed and we show the influence of permutational symmetry on the probability of coincidence of pairs. A special case of this correlation is the well‐known Fermi hole.