Fluctuations beyond the Gutzwiller approximation in the slave-boson approach

We study the Hubbard model through a functional-integral formulation proposed by Kotliar and Ruckenstein. A careful use of the U(1${)}^{\otimes 3}$ gauge symmetry of the bosonized action allows us to compute the complete one-loop correction to the free energy in the case of half-filled band. We extract the effective mass of the fermion in the metallic phase and show that the noninteracting limit is not recovered for vanishing on-site repulsion. The bosonic Hamiltonian must be adjusted order by order in perturbation theory.