Effective lattice actions for correlated electrons.

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 bondcharge model are also discussed. 71.20.Ad, 75.10.Lp, 74.65.+n. Typeset using REVTEX 1 The investigation of the nature of the ground–state and of the low–lying excitations of strongly correlated electron systems is a fundamental problem of the modern many–body theory. The standard model of correlated electrons on a lattice is the Hubbard Hamiltonian