Higher-derivative Lagrangians, nonlocality, problems, and solutions

Higher-derivative theories are frequently avoided because of undesirable properties, yet they occur naturally as corrections to general relativity and cosmic strings. We discuss some of their more interesting and disturbing problems, with examples. A natural method of removing all the problems of higher derivatives is reviewed. This method of "perturbative constraints" is required for at least one class of higher-derivative theories—those which are associated with nonlocality. Nonlocality often appears in low-energy theories described by effective actions. The method may also be applied to a wide class of other higher-derivative theories. An example system is solved, exactly and perturbatively, for which the perturbative solutions approximate the exact solutions only when the method of "perturbative constraints" is employed. Ramifications for corrections to general relativity, cosmic strings with rigidity terms, and other higher-derivative theories are explored.