Asymptotic Renormalization: Complete Quantum Electrodynamics

Wick ordering is frequently invoked in canonical quantum field theory as a device to control vacuum fluctuations and to simplify perturbation theory. In four-dimensional QED, however, the ultraviolet divergences of physical relevance are not removed by normal ordering, and additional pathologies occur for local composite operators, notably in current commutators and gauge invariance constraints. We show that in gauge-invariant entire-function UV completions, ultraviolet finiteness and quasi-locality are achieved at the level of propagators and observables. In this setting the operational role of Wick ordering as a divergence subtraction is eliminated where loop integrals are absolutely convergent, and regulated composite operators are defined by covariant smearing through an entire function of the d'Alembertian. Wick ordering remains only as an optional finite convention relative to a chosen state, rather than a structural necessity.