Analytic Perturbative Approach to QCD

A technique called analytic perturbation theory, which respects the required analytic properties, consistent with causality, is applied to the definition of the running coupling in the timelike region, to the description of inclusive $\tau$-decay, to deep-inelastic scattering sum rules, and to the investigation of the renormalization scheme ambiguity. It is shown that in the region of a few GeV the results are rather different from those obtained in the ordinary perturbative description and are practically renormalization scheme independent.