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

Sven Zschocke·Guenter Plunien·Gerhard Soff
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Abstract

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 b e 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 propagat or. This simplifies significantly calculations in bound state quantum electrodynamis . As one result of our paper the use of the BPHZ-approach in bound state QED is established.

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Sven Zschocke, Guenter Plunien, Gerhard Soff. 2002-04-10. Renormalization of the two-photon vacuum polarization and the self energy vacuum polarization for a tightly bound electron. https://doi.org/10.1007/s10053-002-8865-5

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