Study of a toy model and its relation to the Hubbard model with infinite range hopping

A toy model of strongly correlated fermions is studied using Green function and functional integration methods. The model exhibits a metal-insulator transition as the interaction is varied. In the case of unrestricted hopping is established the equivalence of the model with the Hubbard model with infinite range hopping. The generalization to the case with $N$ components is made.