Perturbation theory in large order for some elementary systems

Reasons for understanding the general problem of perturbation theory in large order are discussed. It is shown that the behavior of perturbation theory in larger order is generally very simple because it reflects just the semiclassical content of the theory. Many simple examples are given, including some graph‐counting problems. The behavior of mass‐renormalized perturbation series for some very simple field‐theory models is examined. It is shown that mass renormalization hardly affects the large‐order behavior of a weak‐coupling perturbation series. However, in a strong‐coupling perturbation series mass renormalization has a dramatic effect.