New Renormalization Scheme of Vacuum Polarization in QED

TL;DR

This paper proposes a new renormalization scheme for vacuum polarization in QED, arguing that the conventional approach's finite contributions lead to discrepancies with experimental hyperfine splitting data.

Contribution

It introduces a novel renormalization method that excludes certain finite contributions of the photon self-energy in QED, challenging traditional gauge invariance assumptions.

Findings

Finite contributions of vacuum polarization affect hyperfine splitting.

The new scheme aligns theoretical predictions with experimental data.

Traditional quadratic divergence treatment may be reconsidered.

Abstract

We examine the vacuum polarization contribution in the renormalization scheme of QED. Normally, the quadratic divergence term is discarded under the condition that the counter term of the Lagrangian density should be gauge invariant. Here, it is shown that the whole contribution of the photon self-energy should not be considered for the renormalization procedure. In fact, the finite contribution of the renormalization in the vacuum polarization is shown to give rise to the hyperfine splitting energy which disagrees with the experimental observation in hydrogen atom. For the treatment of the vacuum polarization, we present a new renormalization scheme of the photon self-energy diagram.