  The finite temperature dynamical response function including the dynamical
local field is derived within a quasiparticle picture for interacting one-,
two- and three dimensional Fermi systems. The correlations are assumed to be
given by a density dependent effective mass, quasiparticle energy shift and
relaxation time. The latter one describes disorder or collisional effects. This
parameterization of correlations includes local density functionals as a
special case and is therefore applicable for density functional theories. With
a single static local field, the third order frequency sum rule can be
fulfilled simultaneously with the compressibility sum rule by relating the
effective mass and quasiparticle energy shift to the structure function or pair
correlation function. Consequently, solely local density functionals without
taking into account effective masses cannot fulfill both sum rules
simultaneously with a static local field. The comparison to the Monte-Carlo
data seems to support such quasiparticle picture.
