Some aspects of self-consistent propagator theories

A general method for constructing bases for operator manifolds for any propagator, which satisfy ``vacuum annihilation conditions'' (VAC's) is developed. This approach is based on the observation that if the transformation of the unperturbed ground state to the correlated ground state is represented as a rotation in the Fock space, the corresponding rotation induced in the basis of the concerned operator space would generate a basis which satisfies VAC's on the correlated ground state. The associated requirements for the Hermiticity of superoperator Hamiltonian would also be met in this new basis. The proposed method is noniterative in that, once the form of the ground-state function is specified, the expansion of the operator manifold satisfying VAC's on the ground state does not require any iterative readjustment. The resultant propagators in this approach are fully linked. It is shown that this theory is equivalent to a propagator formalism in terms of hole- and particle-creation and/or annihilation operators with a modified effective Hamiltonian. The self-consistent electron and polarization propagators are considered as examples, and their underlying perturbative structures are analyzed. The role of density shift operators and higher-rank operators are discussed.