Evidence for the Absence of Regularization Corrections to the Partial-Wave Renormalization Procedure in One-Loop Self-Energy Calculations in External Fields

The equivalence of the covariant renormalization and the partial-wave
renormalization (PWR) approaches is proven explicitly for the
one-loop self-energy (SE) correction of a bound electron state in
the presence of external perturbation potentials.
No "spurious" correction terms to the noncovariant PWR scheme are
generated for Coulomb-type screening potentials and for external
magnetic fields.
It is shown that in numerical calculations of the SE with Coulombic
perturbation potential spurious terms result from an improper treatment
of the unphysical high-energy contribution.
A method for performing PWR utilizing the relativistic B-spline
approach for construction of the Dirac spectrum in external magnetic
fields is proposed.
This method is applied for calculating QED corrections to the
bound-electron g factor in H-like ions.
Within a level of accuracy of about 0.1 % no spurious
terms are generated in numerical calculations of the SE in magnetic fields