Renormalization of the two-photon vacuum polarization and the self energy vacuum polarization for a tightly bound electron

摘要

The renormalization method of Bogoljubov-Parasiuk-Hepp-Zimmermann (BPHZ) isused in order to derive the renormalized energy shift due to the gaugeinvariant K\"all\'en-Sabry diagram of the two-photon vacuum polarization (VPVP)as well as the self energy vacuum polarization S(VP)E beyond the Uehlingapproximation. It is outlined, that no outer renormalization is required forthe two-photon vacuum polarization and that only the inner renormalization hasto b e accomplished. It is shown that the so-called nongauge invariant spuriousterm is absent for a wide class of vacuum polarization (VP) diagrams if oneapplies the widely used spherical expansion of bound and free-electron propagator. This simplifies significantly calculations in bound state quantumelectrodynamis . As one result of our paper the use of the BPHZ-approach inbound state QED is established.