  We 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.
