On Field Theories with Non-Localized Action

It is investigated whether suitable generalizations of the field equations of current field theories to equations of higher order may be of help in eliminating the divergent features of the present theory. It turns out to be difficult, if feasible, to reconcile in this way the requirements of convergence, of positive definiteness of the free field energy, and of a strictly causal behavior of the state vector of a physical system. Progress may perhaps be made by relinquishing the condition of unlimited localizability of any space time event.