Summing perturbation expansions by means of renormalization group considerations

Renormalization group considerations are used to sum divergent perturbation expansions encountered in QCD or other quantum field theories. The method works even in the case when these expansions, considered in a fixed renormalization scheme (RS), are factorially divergent and of asymptotically constant sign. The results assume the form of convergent (under certain circumstances) expansions in a set of functions of a free parameter χ which specifies the procedure involved. It is argued that the relation of the results to conventional, formal perturbation expansions in a fixed RS, in fact suggests the physical interpretation of this parameter and specifies its value. (author). 2 figs., 12 refs