  We present an exact, unconstrained representation of the electron operators
in terms of operators of opposite statistics. We propose a path--integral
representation for the $t$-$J$ model and introduce a parameter controlling the
semiclassical behaviour. We extend the functional approach to the Hubbard model
and show that the mean--field theory is equivalent to considering, at
Hamiltonian level, the Falikov--Kimball model. Connections with a bond-charge
model are also discussed.
