Modified propagators in field theory (with application to the anomalous magnetic moment of the nucleon)

Many attempts have been made to improve upon the perturbation expansion in meson-field theories, one such attempt being the introduction of modified propagators S$_{F}^{\prime}$ and $\Delta _{F}^{\prime}$. It is shown in this paper that the introduction of these new propagators (or at least in the form that has been proposed) creates new infinities which cannot be removed by renormalization. These new infinities are due to new complex poles of the modified propagators. A tentative prescription is put forth to get over these new difficulties, but it is still intimately connected with the perturbation expansion. Unfortunately, the prescription does not give an unambiguous answer. A particular S$_{F}^{\prime}$ is used in the calculation of the anomalous magnetic moment of the nucleon. The results obtained are no better than those of other workers. However, there are many reasons why this may be the case. It is also shown that the subseries which arises in this case leads, at best, to an asymptotic expansion in the coupling constant. The nature of the singularity at zero coupling is found.