  The Kotliar and Ruckenstein slave-boson representation of the Hubbard model
allows to obtain an approximation of the charge dynamical response function
resulting from the Gaussian fluctuations around the paramagnetic saddle-point
in analytical form. Numerical evaluation in the thermodynamical limit yields
charge excitation spectra consisting of a continuum, a gapless collective mode
with anisotropic zero-sound velocity, and a correlation induced high-frequency
mode at $\omega\approx U$. In this work we show that this analytical expression
obeys the particle-hole symmetry of the model on any bipartite lattice with one
atom in the unit cell. Other formal aspects of the approach are also addressed.
