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

It has been a long-standing problem in $N$-electron systems as to how solve the Dyson equation with quasiparticle wave functions defined $\ensuremath{\langle}\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Psi}}}_{0}^{N}\phantom{\rule{0.16em}{0ex}}|\phantom{\rule{0.16em}{0ex}}{\ensuremath{\psi}}_{s}(\mathbit{r})\phantom{\rule{0.16em}{0ex}}|\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Psi}}}_{\ensuremath{\nu}}^{N+1}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rangle}$ and $\ensuremath{\langle}\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Psi}}}_{\ensuremath{\mu}}^{N\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}|\phantom{\rule{0.16em}{0ex}}{\ensuremath{\psi}}_{s}(\mathbit{r})\phantom{\rule{0.16em}{0ex}}|\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Psi}}}_{0}^{N}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rangle}$, which are not mutually orthogonal have norm less than 1. We show that without multiple excitations can exactly be normalized unity owing Ward identity vertex function $(\mathbit{q},{\ensuremath{\omega}}^{\ensuremath{'}}\ensuremath{-}\ensuremath{\omega})\ensuremath{\rightarrow}0$, although they necessarily orthogonal. Since satisfy an eigenvalue hermitized self-energy due Baym-Kadanoff's conservation laws, present theory regarded extension of Kohn-Sham density functional theory, correlated, interacting, one-electron orbitals.