  We reconsider the strong-coupling expansion for the Hubbard model recently
introduced by Sarker and Pairault {\it et al.} By introducing slave particles
that act as projection operators onto the empty, singly occupied and doubly
occupied atomic states, the perturbation theory around the atomic limit
distinguishes between processes that do conserve or do not conserve the total
number of doubly occupied sites. This allows for a systematic $t/U$ expansion
that does not break down at low temperature ($t$ being the intersite hopping
amplitude and $U$ the local Coulomb repulsion). The fermionic field becomes a
two-component field, which reflects the presence of the two Hubbard bands. The
single-particle propagator is naturally expressed as a function of a $2 \times
2$ matrix self-energy. Furthermore, by introducing a time- and
space-fluctuating spin-quantization axis in the functional integral, we can
expand around a ``non-degenerate'' ground-state where each singly occupied site
has a well defined spin direction (which may fluctuate in time). This formalism
is used to derive the effective action of charge carriers in the lower Hubbard
band to first order in $t/U$. We recover the action of the t-J model in the
spin-hole coherent-state path integral. We also compare our results with those
previously obtained by studying fluctuations around the large-$U$ Hartree-Fock
saddle point.
