  The gauge symmetry group of any slave boson representation allows to gauge
away the phase of bosonic fields. One benefit of this radial field formulation
is the elimination of spurious Bose condensations when saddle-point
approximation is performed. Within the Kotliar-Ruckenstein representation,
three of the four bosonic fields can be radial while the last one has to remain
complex. In this work, we present the procedure to carry out the functional
integration involving constrained fermionic fields, complex bosonic fields, and
radial bosonic fields. The correctness of the representation is verified by
exactly evaluating the partition function and the Green's function of the
Hubbard model in the atomic limit.
