Some comments on the treatment of symmetry properties in perturbation theory
Per‐Olov Löwdin · International Journal of Quantum Chemistry · 2009
The treatment of constants of motion and symmetry properties in partitioning technique and perturbation theory is briefly discussed. A constant of motion may be characterized by a set of projection operators {QQ} forming a resolution of the identity and leading to a splitting of the Hilbert space into orthogonal and non-interacting subspaces. It is shown that, in the partitioning technique, it is sufficient to consider only one such subspace at a time, which is a considerable simplification. The treatment may be extended to perturbation theory ℋ︁ = ℋ︁ 0 + V, and it is shown that the unperturbed Hamiltonian ℋ︁ 0 enters the formalism only in the form of the reduced resolvents occurring in ordinary perturbation theory. It is emphasized that, even if the infinite-order expressions are unique, the finite-order expansions in the perturbation V are ambiguous, and the relation between various forms is studied.