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The finite temperature dynamical response function including the dynamicallocal field is derived within a quasiparticle picture for interacting one-,two- and three dimensional Fermi systems. The correlations are assumed to begiven by a density dependent effective mass, quasiparticle energy shift andrelaxation time. The latter one describes disorder or collisional effects. Thisparameterization of correlations includes local density functionals as aspecial case and is therefore applicable for density functional theories. Witha single static local field, the third order frequency sum rule can befulfilled simultaneously with the compressibility sum rule by relating theeffective mass and quasiparticle energy shift to the structure function or paircorrelation function. Consequently, solely local density functionals withouttaking into account effective masses cannot fulfill both sum rulessimultaneously with a static local field. The comparison to the Monte-Carlodata seems to support such quasiparticle picture.Comment: 16 pages, 5 Fi

Dynamical local field, compressibility, and frequency sum rules for quasiparticles