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The Hubbard model with finite on-site repulsion U is studied via thefunctional-integral formulation of the four-slave-boson approach by Kotliar andRuckenstein. It is shown that a correct treatment of the continuum imaginarytime limit (which is required by the very definition of the functionalintegral) modifies the free energy when fluctuation (1/N) corrections beyondmean-field are considered. Our analysis requires us to suitably interpret theKotliar and Ruckenstein choice for the bosonic hopping operator and to abandonthe commonly used normal-ordering prescription, in order to obtain meaningfulfluctuation corrections. In this way we recover the exact solution at U=0 notonly at the mean-field level but also at the next order in 1/N. In addition, weconsider alternative choices for the bosonic hopping operator and test themnumerically for a simple two-site model for which the exact solution is readilyavailable for any U. We also discuss how the 1/N expansion can be formallygeneralized to the four-slave-boson approach, and provide a simplifiedprescription to obtain the additional terms in the free energy which result atthe order 1/N from the correct continuum limit.Comment: Changes: Printing problems (due to non-standard macros) have been  removed, 44 page

Correct continuum limit of the functional-integral representation for the four-slave-boson approach to the Hubbard model: Paramagnetic phase