  The three-component ab-plane optical conductivity of the high-T_c cuprates is
derived using the gauge invariant response theory, and compared to the data
previously obtained from the optical reflectivity measurements in the La_2CuO_4
based families. The valence electrons are described by the Emery three-band
model with the antiferromagnetic correlations represented by an effective
single-particle potential. In the 0 < delta < 0.3 doping range, it is shown
that the total spectral weight of the three-band model is shared between the
intra- and interband channels nearly in equal proportions. At optimum doping,
the low-frequency conductivity has a (non-Drude) nearly single-component form,
which transforms with decreasing doping into a two-component structure. The
mid-infrared spectral weight is found to be extremely sensitive to the symmetry
of the effective single-particle potential, as well as to the doping level. The
gauge invariant form of the static and elastic Raman vertices is determined,
allowing explicit verification of the effective mass theorem and the related
conductivity sum rules.
