The validity of the optical sum rules has been addressed eversince and
was always matter of debate. Particularly controversial is the proof
that the partial sum rules can be extended to both optical conductivit
y and energy loss function. We show in this paper that for both transv
erse (optical conductivity) and longitudinal (energy loss function) ab
sorption processes the corresponding sum rule can be theoretically est
ablished and through appropriate conditions for the integration limits
exactly verified. We also focus our attention on the one-dimensional
case within the microscopic Hubbard model. An application of these con
cepts to the quasi one-dimensional systems, for which we have chosen t
he organic (TMTSF)(2)PF6 material, will also be presented.