  In strongly correlated electron systems the constraint which prohibits the
double electron occupation at local sites can be realized by either the
infinite Coulomb interaction or the correlated hopping interaction described by
the Hubbard operators, but they both render the conventional field theory
inapplicable. Relaxing such the constraint leads to a class of correlated
hopping models based on the deformed Hubbard operators which smoothly
interpolate the locally free and strong coupling limits by a tunable
interaction parameter $0\leq \lambda\leq 1$. Here we propose a coherent state
path integral approach appropriate to the deformed Hubbard operators for {\it
arbitrary} $\lambda$. It is shown that this model system exhibits the
correlated Fermi liquid behavior characterized by the enhanced Wilson ratio for
all $\lambda$. It is further found that in the presence of on-site Coulomb
interaction a finite Mott gap appears between the upper and lower Hubbard
bands, with the upper band spectral weight being heavily reduced by $\lambda$.
Our approach stands in general spatial dimensions and reveals an unexpected
interplay between the correlated hopping and the Coulomb repulsion.
