  We define Landau quasi-particles within the Gutzwiller variational theory,
and derive their dispersion relation for general multi-band Hubbard models in
the limit of large spatial dimensions D. Thereby we reproduce our previous
calculations which were based on a phenomenological effective single-particle
Hamiltonian. For the one-band Hubbard model we calculate the first-order
corrections in 1/D and find that the corrections to the quasi-particle
dispersions are small in three dimensions. They may be largely absorbed in a
rescaling of the total band width, unless the system is close to half band
filling. Therefore, the Gutzwiller theory in the limit of large dimensions
provides quasi-particle bands which are suitable for a comparison with real,
three-dimensional Fermi liquids.
