New Renormalization Scheme of Vacuum Polarization in QED

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.