Slave bosons in radial gauge: the correct functional integral representation and inclusion of non-local interactions

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.