Renormalization of the two-photon vacuum polarization and the self energy vacuum polarization for a tightly bound electron
Institut für Theoretische Physik,
Technische Universität Dresden, Mommsenstrasse 13,
01062 Dresden, Germany
Published online: 15 May 2002
The renormalization method of Bogoljubov-Parasiuk-Hepp-Zimmermann (BPHZ) is used in order to derive the renormalized energy shift due to the gauge invariant Källén-Sabry diagram of the two-photon vacuum polarization (VPVP) as well as the self energy vacuum polarization S(VP)E beyond the Uehling approximation. It is outlined, that no outer renormalization is required for the two-photon vacuum polarization and that only the inner renormalization has to be accomplished. It is shown that the so-called nongauge invariant spurious term is absent for a wide class of vacuum polarization (VP) diagrams if one applies the widely used spherical expansion of bound and free-electron propagator. This simplifies significantly calculations in bound state quantum electrodynamics. As one result of our paper the use of the BPHZ-approach in bound state QED is established.
PACS: 31.30.Jv – Relativistic and quantum electrodynamic effects in atoms and molecules
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002