  The Hubbard model with finite on-site repulsion U is studied via the
functional-integral formulation of the four-slave-boson approach by Kotliar and
Ruckenstein. It is shown that a correct treatment of the continuum imaginary
time limit (which is required by the very definition of the functional
integral) modifies the free energy when fluctuation (1/N) corrections beyond
mean-field are considered. Our analysis requires us to suitably interpret the
Kotliar and Ruckenstein choice for the bosonic hopping operator and to abandon
the commonly used normal-ordering prescription, in order to obtain meaningful
fluctuation corrections. In this way we recover the exact solution at U=0 not
only at the mean-field level but also at the next order in 1/N. In addition, we
consider alternative choices for the bosonic hopping operator and test them
numerically for a simple two-site model for which the exact solution is readily
available for any U. We also discuss how the 1/N expansion can be formally
generalized to the four-slave-boson approach, and provide a simplified
prescription to obtain the additional terms in the free energy which result at
the order 1/N from the correct continuum limit.
