Evidence for the absence of regularization corrections to the partial-wave renormalization procedure in one-loop self energy calculations in external fields

Details Evidence for the absence of regularization corrections to the partial-wave renormalization procedure in one-loop self energy calculations in external fields Evidence for the absence of regularization corrections to the partial-wave renormalization procedure in one-loop self energy calculations in external fields

2000-06-19

arxiv.org/abs/hep-ph/0006220v2

Phys.Rev. A65 (2002) 042110

Physics

High Energy Physics

High Energy Physics - Phenomenology

22 pages, LaTeX, 1 figure

Scientific paper

10.1103/PhysRevA.65.042110

The equivalence of the covariant renormalization and the partial-wave renormaliz ation (PWR) approach is proven explicitly for the one-loop self-energy correction (SE) of a bound electron state in the presence of external perturbation potentials. No spurious correctio n terms to the noncovariant PWR scheme are generated for Coulomb-type screening potentia ls 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 the PWR utilizing the relativistic B-spline approach for the 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 the level of accuracy of about 0.1% no spurious terms are generated in numerical calculations of the SE in magnetic fields.

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