Investigation on regulators in quantum electrodynamics

We present in this work three models which are able to suppress the divergences of approximate versions of Quantum Electrodynamics.It is indeed argued that, in view of the smallness of the fine structure constant, not only the first terms of a perturbation expansion, or of an expansion according to the number of particles involved in intermediate states, gives a fair approximattonbut furthermore, that it is in these terms that a breakdown of electrodynamics should be sought. Our goal is to connect the high energy behaviour of relevant physical processes with the suppression of the divergences. Our goal is to connect the high energy behaviour of relevant physical processes with the suppression of the divergences. The first model assumes the existence of a photon cut off, whose observable consequences are clearly stated, and of a fermion out off which, although unable to give a satisfactory description of phenomena involving virtual fermions, points to the conclusicn that these have no obvious connection with the creat~ion of virtual pairs in vacuo. The second model is based on formal analytic relation- ships exhibited by the lowest order perturbation theory and connects the divergences with the high behaviour of the phenomena which, while they are well described here were left out by the first model. The third model, aiming at a better understanding of the preceding onecontradicts its theoretical basis without necessarily invalidating the observable conse- quences that were drawn from it.