The road to Stueckelberg's covariant perturbation theory as illustrated bysuccessive treatments of Compton scattering

We review the history of the road to a manifestly covariant perturbative ca lculus within quantum electrodynamics from the early semi-classical results of the mid-twenties to the complete formalism of Stueckelberg in 1934. We choose as our case study the calculation of the cross-section of the Compto n effect. We analyse Stueckelberg's paper extensively. This is our first co ntribution to a study of his fundamental contributions to the theoretical p hysics of the twentieth century. Copyright (C) 1999 Elsevier Science Ltd. A ll rights reserved.