Fermi–linearization Scheme for Itinerant Electrons with Clifford Variables

We propose here an alternative interpretation of the fermi-linarization approach to interacting electron systems, based on the requirement that the coefficients of the linearized operators are Clifford-like variables, whose anticommutator equals an unknown constant c. We apply the approximation to the Falicov-Kimball model, explicitly solving the self-consistency equation for the unknown, which turns out to behave as an order parameter. We discuss its relation with a metal-insulator transition and some thermodynamical quantities. In particular we show that our approximation in the T = 0 limit reproduces exactly the Gutzwiller results for the Hubbard model. P.A.C.S. # 05.30.Fk 71.10.+x