2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/87756We review the history of the road to a manifestly covariant perturbative calculus within quantum electrodynamics from the early semi-classical results of the mid-twenties to the complete formalism of Stueckelberg in 1934. We chose as our case study the calculation of the cross-section of the Compton effect. We analyse Stueckelberg's paper extensively. This is our first contribution to a study of his fundamental contributions to the theoretical physics of twentieth century.This paper is a "working-physicist" version of a paper to be published in Studies in History and Philosophy of Modern PhysicsHistory and Philosophy of Physicstext