Gutzwiller projection for bosons

We apply Gutzwillers variational method to the interacting Bose lattice gas. In contrast with the Fermi case, the Gutzwiller wave function for bosons can be treated with no further approximation in several limits. Furthermore, this wave function can be shown to be exact for large dimensionality, and also in arbitrary dimension for suitably chosen short-range interactions. At densities commensurate with the lattice, a superfluid-insulator transition is found. These results are compared with the fermionic case, and are applied to several interacting-boson systems.