Renormalization-scheme-independent perturbation theory by resumming logarithms

Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by reexpanding with respect to a scheme invariant quantity. Furthermore, we investigate whether the potentially large logarithms in such an expansion cause inaccuracy and how this can be improved.