In most branches of theoretical physics exact results are rare and
almost all interesting physical quantities can be calculated only
within some perturbative approach. Unfortunately, in quantum field
theory the canonical perturbation expansion is plagued by infinities
and - after renormalization - by the dependence of the results on an
unphysical parameter (the renormalization scale (RS)). This yields a
certain amount of arbitrariness of the theoretical forecasts and
makes comparison with experimental data somewhat problematic. The RS
dependence is particularly striking in finite temperature field
theory due to the resummation process needed there. I will outline
an attempt to remove the Renormalization Scale dependence of ordinary
perturbation expansions (when truncated at some finite order) by
converting the power series into a more general approximation scheme.
Technical details will largely be avoided and the talk will be geared
for experimentalists as well as theorists.