  An ensemble Green's function formalism, based on the von Neumann density
matrix approach, to calculate one-electron excitation spectra of a
many-electron system with degenerate ground states is proposed. A set of
iterative equations for the ensemble Green's function and self-energy is
derived and a simplest approximation corresponding to an ensemble $GW$
approximation is naturally obtained. The derivation is based on the Schwinger
functional derivative technique and does not assume any adiabatic connection
between a noninteracting and an interacting ground state.
