Abstract
The unitary group formulation is a viable alternative to the Slater determinant and second quantized methods when the Hamiltonian is spinfree. Here the Hamiltonian is expressed as a second degree polynomial in the infinitesimal generators of U(ρ) where p is the number of spatial (spin-free) orbitals. Each irreducible space of U(ρ) is invariant under this Hamiltonian and is uniquely characterized by a Young diagram which, for the Pauli allowed spaces, supplies both particle and spin quantum numbers. Each irreducible space is spanned by a set of orthonormal Gel’fand states and the Hamiltonian matrix elements are conveniently calculated by the graphical unitary approach (GUGA). The many-body approximation theories (single and multiconfiguration restricted Hartree Fock, RPA, perturbation, coupled cluster and effective Hamiltonian theories) have been given a unitary group formulation
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