The Electromagnetic Interactions

We briefly review the birth of renormalisation theory at the 1947 Shelter Island conference. We study the particular case of quantum electrodynamics in the example of an electron scattered by an external electromagnetic field. We give the general form of the amplitude in terms of form factors. At one loop the amplitude has both ultraviolet and infrared divergences. We show how to absorb the ultraviolet divergences by means of counterterms whose values are determined by the renormalisation conditions. We also show that at one loop order the electron anomalous magnetic moment is free of divergences, ultraviolet as well as infrared, and present its explicit calculation.