$S$-Matrix Theory of Electromagnetic Interactions

This paper studies the possibility of applying the principles of the $S$-matrix theory to electrodynamics. By using an approximation scheme different from that in the strong interactions, many results of quantum electrodynamics can indeed be reproduced. While the calculations of electrodynamical problems can be carried out in a more straightforward and less laborious way in the $S$-matrix theory, there still are some basic difficulties. However, as far as scattering processes and the anomalous magnetic moment are concerned, there is complete identity (up till fourth order) between the two methods. The bound-state problem, infrared divergence, and the many-particle problem remained unsettled.