Optimization and the convergence of perturbation series

This thesis is concerned with the possible sums of perturbation series in mass- less, renormalizable field theories. It shows that, given a free choice of scheme, the limit of the sequence of approximants is arbitrary. Restricting the choice to finite schemes, in particular "zero schemes", yields a perturbatively unique limit to the sequence of approximants. An operational method for calculating perturbative expansions in the class of zero schemes is discussed. A comparison of various optimization schemes is given for a few phenomenological examples in QCD and QED.