The very rapid development of field theory and especially quantum electrodynamics during the last years is based upon the conceptions of mass-and charge-renormalizations.
These devices were originally designed to overcome the divergence difficulties encountered in the older formulations of field theory. It has been known for more than twenty years that the displacement of the energy of, e.g., an electron due to its interaction with the radiation field -i.e. the self-energy of the electron -is infinite, if it is calculated with the aid of a straight-forward application of perturbation theory. This fact had been a stumbling block until 1947 when it was recognized i) that at least the main part of the infinity could be incorporated in the mass of the electron, thus producing no observable effect. The remainder of the energy-displacement could be calculated and compared with experimental results. Later refinements of the method of calculationz)-4) have confirmed the general spirit of the first attack and nowadays there is little doubt that the mathematical framework of quantum electrodynamics contains something which corresponds closely to physical reality. Through the fundamental work by S c h w i n g e r ") and others ") we have today a very beautiful formal mathematics with the aid of which it is possible to eliminate systematically the infinities appearing during the calculations and to extract physically meaningful results from the remaining expressions provided that perturbation theory is used the whole time. From the point of view of comparison with experimental results perturbation theory is quite satisfactory and no significant dis-*) This work has been performed at the