Scalar QED is investigated in the framework of causal perturbation the
ory. This approach which is ultraviolet finite differs from the conven
tional formalism because the inductive construction starts from the si
mple first-order interaction, without the term quadratic in the electr
omagnetic potential. The latter appears in the process of distribution
splitting as a consequence of gauge invariance. In this way normaliza
bility, gauge invariance and unitarity can be rigorously proven.