Permutational Symmetry of Reduced Density Matrices

Abstract

The usual restriction on the permutational symmetry of density matrices is removed. An Nth‐order density matrix of general permutational symmetry is reduced and the symmetry of the resulting pth‐order density matrix is found. This gives rise to necessary conditions for the N‐representability of spin‐free density matrices. We indicate the importance of these results for symmetry under the groups GL(n), U(n), and SU(n). We generalize the question of N‐representability to the tensor algebra, where contraction of tensors plays the role of reduction of density matrices. Symmetry properties of the tensors are studied and density matrices are considered as special cases.