  Using an imaginary-time path integral approach, we develop the perturbation
theory suited to the boson Hubbard model, and apply it to calculate the effects
of a dilute gas of spin-polarized fermions weakly interacting with the bosons.
The full theory captures both the static and the dynamic effects of the
fermions on the generic superfluid-insulator phase diagram. We find that, in a
homogenous system described by a single-band boson Hubbard Hamiltonian, the
intrinsic perturbative effect of the fermions is to generically suppress the
insulating lobes and to enhance the superfluid phase.
