Summary
Scalar QED is investigated in the framework of causal perturbation theory. This approach which is ultraviolet finite differs from the conventional formalism because the inductive construction starts from the simple first-order interaction, without the term quadratic in the electromagnetic potential. The latter appears in the process of distribution splitting as a consequence of gauge invariance. In this way normalizability, gauge invariance and unitarity can be rigorously proven.
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Dütsch, M., Krahe, F. & Scharf, G. Scalar QED revisited. Nuov Cim A 106, 277–308 (1993). https://doi.org/10.1007/BF02771445
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DOI: https://doi.org/10.1007/BF02771445