Effective Mode Structure in Quantum Electrodynamics Replacing Ultraviolet Renormalization

In order to avoid renormalization in Bethe's first calculation of the Lamb shift, it is possible to find a modified mode structure of the vacuum. As a consequence, mode counting in quantum electrodynamics is re-examined for localized interactions. I show that ultraviolet divergences can be removed by a Lorentz-covariant modification of the effective mode density while preserving the Ward identity. The infrared (IR) structure of the theory remains unchanged, and loop integrals become ultraviolet finite without counterparts. After fixing the physical electron mass and charge, all on-shell observables agree with the standard renormalized results. The approach is illustrated by the anomalous magnetic moment and the leading contribution to the Lamb shift, and suggests a natural extension to more general field theories.