Normalization of exact quasiparticle wave functions in the Green's function method guaranteed by the Ward identity

Abstract

It has been a long-standing problem in N-electron systems as to how to solve the Dyson equation with the quasiparticle wave functions defined as (ψ0N|ψs(r)|ψνN+1) and (ψμN-1|ψs(r)|ψ0N), which are not mutually orthogonal and have a norm less than 1. We show that quasiparticle wave functions without multiple excitations can exactly be normalized to unity owing to the Ward identity and the vertex function in (q,ω′-ω)→0, although they are not necessarily mutually orthogonal. Since they satisfy an eigenvalue equation with the hermitized self-energy due to Baym-Kadanoff's conservation laws, the present theory can be regarded as an extension of the Kohn-Sham density functional theory, with correlated, interacting, one-electron orbitals.