  We introduce a new path integral representation for slave bosons in the
radial gauge which is valid beyond the conventional fluctuation corrections to
a mean-field solution. For electronic lattice models, defined on the
constrained Fock space with no double occupancy, all phase fluctuations of the
slave particles can be gauged away if the Lagrange multipliers which enforce
the constraint on each lattice site are promoted to time-dependent fields.
Consequently, only the amplitude (radial part) of the slave boson fields
survives. It has the special property that it is equal to its square in the
physical subspace. This renders the functional integral for the radial field
Gaussian, even when non-local Coulomb-type interactions are included. We
propose i) a continuum integral representation for the set-up of further
approximation schemes, and ii) a discrete representation with an Ising-like
radial variable, valid for long-ranged interactions as well. The latter scheme
can be taken as a starting point for numerical evaluations.
