Perturbation Theory and Self-Mass Insertions

First-order perturbation corrections to strong-interaction amplitudes are considered in the context of quantum field theory. It is shown that such corrections may be expressed entirely in terms of on-mass-shell matrix elements of the unperturbed system, matrix elements which are evaluated at the unperturbed mass. The general method is illustrated by a detailed discussion of form-factor corrections. In particular, the method is applied to the conserved-vector form factor of a meson multiplet, and it is shown that the Ademollo-Gatto theorem holds only if the perturbation is local. The violation of this theorem, which occurs in the electromagnetic correction to pion $\beta$ decay, is discussed.