Symmetric Group Approach to the Many-Electron Problem

The eigenvalue problem of a Hamiltonian represented in a finite-dimensional model space selected as a spin-adapted N-electron subspace of the 2K-spinorbital Fock space is analyzed. The symmetric group { S}_N is a very convenient framework for this analysis. The resulting approach is known as the symmetric group approach (SGA) to the N-electron problem. Its applications to the construction of a basis in the model space, to the evaluation of matrix elements of spin-independent and of spin-dependent operators and to solution of the eigenvalue problem of the Hamiltonian are briefly reviewed. Recently developed applications of the symmetric group to studies of the Heisenberg Hamiltonian spectra are also mentioned.