  The dynamic charge susceptibility and the optical conductivity are calculated
in the planar t-J model within the memory function method, working directly in
terms of Hubbard operators. The density fluctuation spectrum consists of a
damped sound-like mode for small wave vectors and a broad high energy peak
($\sim t$) for large momenta. The study of the optical conductivity shows that
electron scattering from spin fluctuations leads to the Drude-frequency
dependent relaxation rate which exhibits a crossover from $\omega^{3/2}$
behavior at low frequencies ($\omega <2|\mu|$), to a linear $\omega$-dependence
for frequencies larger than $2|\mu|$. Due to the spin-polaron nature of charge
carriers, extra absorbtions arise starting at a frequency $\omega \agt J$. The
obtained results are in a good agreement with exact diagonalization studies.

Strongly Correlated Electrons;Superconductivity