Convergent Field Theory with Complex Masses

The aim of this paper is to construct a consistent and convergent field theory. For this purpose the propagation functions are improved. The new propagators have to satisfy several conditions. Among these conditions the most interesting ones are "definite norm", "divergenceless" and "causality". It turns out that the new propagators include necessarily complex masses which have very close connection with "causality". In order to examine this problem the propagator is studied carefully in a simple case, and is found to be macrocausal. It is suggested that the theory is connected with the validity of quantum electrodynamics at small distances and could be tested by experiments.