  We generalize the rotationally-invariant formulation of the slave-boson
formalism to multiorbital models, with arbitrary interactions, crystal fields,
and multiplet structure. This allows for the study of multiplet effects on the
nature of low-energy quasiparticles. Non-diagonal components of the matrix of
quasiparticle weights can be calculated within this framework. When combined
with cluster extensions of dynamical mean-field theory, this method allows us
to address the effects of spatial correlations, such as the generation of the
superexchange and the momentum dependence of the quasiparticle weight. We
illustrate the method on a two-band Hubbard model, a Hubbard model made of two
coupled layers, and a two-dimensional single-band Hubbard model (within a
two-site cellular dynamical mean-field approximation).
